game modelling and strategy research on trilateral evolution for...

Research ArticleGame Modelling and Strategy Research on Trilateral Evolutionfor Coal-Mine Operational Safety Production SystemA Simulation Approach

Yan Li 1 Yan Zhang 1 Haifeng Dai 2 and Ziyan Zhao3

1School of Management Xirsquoan University of Science amp Technology Xirsquoan 710054 China2School of Mechanical and Electrical Engineering Xirsquoan Polytechnic University Xirsquoan 710600 China3Finance Department China Construction Integrated Housing (Henan) Co Ltd Zhengzhou 450000 China

Correspondence should be addressed to Yan Zhang yanzhang1008126com

Received 29 June 2019 Accepted 4 December 2019 Published 8 January 2020

Academic Editor Michele Scarpiniti

Copyright copy 2020 Yan Li et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In view of the particularity and high risk of coal mining industry the decision-making behavior of multiple agents inside the coal-mine enterprise plays a very important role in ensuring the safety and sustainable development of coal mining industry eexisting literature studies on coal-mine safety production focus mainly on statically analyzing the game among the external entitiessuch as the government the enterprises themselves and the employees inside the enterprise from a macro perspectiveare short ofresearch on revealing the dynamic interactions among the actors directly involved in the coal-mine accidents and also onproposals for eective interactions that will lead to improved safety outcomes erefore this paper explores the use of evo-lutionary game theory to describe the interactions among the stakeholders in Chinarsquos coal-mine safety production system whichincludes the organization the rst-line miners and the rst-line managers Moreover the paper also explores dynamic sim-ulations of the evolutionary game model to analyze the stability of stakeholder interactions and to identify equilibrium solutions e simulation results show that when certain conditions are met the decision-making behavior of the organization miners andmanagers can evolve into the unique ideal steady state (1 1 1) In addition the strategy portfolio with a relatively high initialproportion of three agents converges more quickly to an ideal state than a relatively low strategy portfolio Moreover the stablestate and equilibrium values are not aected by the initial value changes Finally we nd that the combination of positive incentivepolicies and strict penalties policies can make the evolutionary game system converge to desired stability faster e application ofthe evolutionary game and numerical simulation when simulating the multiplayer game process of coal-mine safety production isan eective way which provides a more eective solution to the safety and sustainable development of coal mining industry

1 Introduction

e Global Coal Market Report (2018ndash2023) jointly orga-nized by the International Energy Agency (IEA) and theNational Energy Group points out that coal is still the coreof the global energy system and global coal demand willremain stable in the next ve years e Coal Market Report2017 jointly issued by the China Oce of the SustainableCities and Communities (SUC) Project and the Interna-tional Energy Agency (IEA) also points out that ensuringthe economic benets and ensuring the safety of coal in-dustry are recent policy priorities In order to ensure the

sustainable development of the coal industry we must payattention to the safety of the coal industry Currently whilethe safety performance of coal mines in China has improvedoverwhelmingly year after year [1 2] coal-mine safety ac-cidents are still frequent and the industry still has an ap-palling record of fatalities [3] e losses caused by coal-mine safety accidents are catastrophic Coal-mine safetyaccidents not only cause huge casualties but also cause hugeeconomic losses and hinder the sustainable development ofcoal mining industry meanwhile they have a strong neg-ative impact on social stability erefore improving coal-mine safety production is the key to promoting the

HindawiComplexityVolume 2020 Article ID 2685238 16 pageshttpsdoiorg10115520202685238

sustainable development of coal mining industry and is oneof the problems that China need to solve urgently

In order to reduce the occurrence of coal-mine safetyaccidents improve the current situation of coal-mine safetyproduction and ensure the sustainable development of coalmining industry domestic and foreign scholars have studiedeffective countermeasures to promote coal-mine safetyproduction from different perspectives and aspects

e first research stream of coal-mine safety productionenhancement focuses on the human factors such as con-trolling the unsafe behavior of miners e unsafe behaviorof miners is the most direct cause of coal-mine safety ac-cidents and the main reason for destroying the normaloperation of coal-mine safety production [4ndash6] e minersalways face a trade-off between work stress for safe operationand psychological benefits for unsafe operation andreaching higher psychological and spiritual benefits mighthave strong substitution effects with safe operationerefore alleviating the work stress response of miners andimproving the safety behavior of them are the key to en-suring the normal operation of coal-mine safety productionAt present most scholars explore the generating mechanismof the unsafe behavior of miners and results indicate that theindividual characteristics (safety awareness knowledge andskills safety attitude physical quality and experience) ofminers [7ndash9] and environmental factors [10ndash12] (workingenvironment equipment environment social environmentfamily environment etc) have significant impact on theminersrsquo behavioral decisions which will in turn affect thesafety production of coal mining enterprises

e second research stream of coal-mine safety pro-duction enhancement focuses on the organizational factors[13ndash15] e organizationrsquos investments in safety culturepropaganda safety training safety regulations and safetyincentives will affect the level of the safety climate and thusaffect the minersrsquo behavioral decisions ultimately affectingthe safety production of coal mining enterprises In shortthe level of safety climate of organization plays an importantrole in the operation of coal-mine safety production and theimprovement level of safety climate depends on the orga-nizationrsquos emphasis and the attention degree on safety[16 17] According to the theory of social exchange [18ndash20]the safety climate level of organization and the behavioraldecision of miners are equivalent and reciprocal At the sametime the supervision of first-line managers also affects thebehavioral decision making of miners And the behavioraldecision-making model of miners [21] indicates that theexpected total value of minersrsquo unsafe behavior is deter-mined by the decision weight function and the psychologicalvalue function and the decision weight function is closelyrelated to the supervision effect of supervisors Before theminers make decisions the supervision effect of supervisorswill affect the minersrsquo expectations of the taskrsquos interests inthe decision making it influences the decision weightfunction and the psychological value function and theninfluences the behavior decision which ultimately affects thesafety production level of coal-mine enterprises And somestudies [22 23] comprehensively analyzed human factorsand organizational factors involved in mining accidents and

determined the relationships among these factors e re-sults showed that the human factors including skill-basederrors routine violations and planned inappropriate op-eration and environmental factors had a higher relativeimportance in the accidents Moreover the environmentalfactors and human factors had a higher influence on unsafeacts

e research streams of the previous two focus on theinfluencing mechanism of internal and external factors(individual characteristics machinery and equipmentworking environment and organization management) oncoal-mine safety production and the ldquopeople-machine-ring-tuberdquo causal system is gradually formed to our knowledgemost of them analyze coal-mine safety production and itsinfluencing factors from static and a single perspective andthey are short of research on the interaction of variousfactors from the perspective of overall system neglecting thesubjective initiative of individual behavior

In order to make up for the above defects the thirdresearch stream of coal-mine safety production enhance-ment focuses on the gaming behaviors of stakeholders eearly game research studies [24ndash27] on coal-mine safetyproduction mainly analyzed the relationship between thecoal-mine regulators and coal enterprise and concluded thatthe coal enterprisersquos inadequate safety investment was thereal cause of the frequent accidents and proposed that thepenalty for the coal enterprisersquos unlawful production shouldbe strengthened in the short term ese studies provide apromising foundation to explain the high incidence of coalaccidents in China and improve the situation of coal-minesafety production However the above research studiesmainly focus on statically analyzing the game between twostakeholders and neglect the dynamic process of game playIn order to explain the dynamic process of coal-mine safetyproduction more systematically and comprehensively Liuet al [28] explored the use of evolutionary game theory todescribe the long-term dynamic process of multiplayer gameplaying in coal-mine safety regulation under the condition ofbounded rationality Furthermore the multiplayer evolu-tionary game was simulated by adopting system dynamics toanalyze the implementation effect of different penaltystrategies on the game process and game equilibrium Topromote the safety education level of Chinarsquos coal miningenterprises the government coal mining enterprises andemployees are included in the evolutionary game model toexplore the game relation and evolutionary path of thedecision-making behavior among the three stakeholders inthe safety management system [29 30] However they focusmainly on analyzing the game between the external entitiessuch as the government the enterprises themselves and theemployees from a macro perspective are short of researchon revealing the dynamic interactions among the actorsdirectly involved in the coal-mine accidents and also onproposals for effective interactions that will lead to improvedsafety outcomes Although Yu et al [31] constructed anevolutionary game model of workersrsquo behavior in coalmining enterprises only the static game between the twoagents such as the managers and miners was consideredActually the stakeholders in coal-mine safety production

2 Complexity

system include the organization the first-line miners andthe first-line managers and the operational system is theprocess in which these game agents interact with each otherin complex environments [32ndash34] In the process of coal-mine safety production the players operate within boundedrationality and their strategy selections are not alwaysunchanged or static instead they change strategies dy-namically by observing and comparing payoffs with othersand adjusting their strategy selections leading the evolu-tionary stable states in the game erefore to help addressthis gap in the research this paper explores the use ofevolutionary game theory to describe the long-term dynamicprocess of multiplayer game playing in coal-mine safetyproduction under the condition of bounded rationalityFurthermore the multiplayer evolutionary game is simu-lated by adopting Matlab simulation technology to analyzeits stability and then effective stability control strategies areproposed and checked based on the simulation analysisincluding the set of stakeholders

e remainder of this paper is organized as followsSection 2 constructs a trilateral evolutionary game model ofcoal-mine safety production and analyzes the stability andbalance of the game model Section 3 presents the three-player evolutionary game simulation based on Matlabsimulation technology and finds the best stable equilibriumpoint Section 4 discusses the effectiveness of simulationresults and internal driving strategy of coal-mine safetyproduction Finally concluding remarks are presented inSection 5

2 Trilateral Game Model of Coal-MineSafety Production

Evolutionary game theory was developed to overcome thedisadvantages of traditional game theory when analyzing thebounded rationality of players and the dynamic process ofgame playing [35ndash39] In the process of coal-mine safetyproduction in China the players are bounded rational andthey change their strategies dynamically by observing andcomparing payoff with others and then adjust their strate-gies erefore evolutionary game theory is more suitablefor studying the long-term dynamic game of bounded ra-tional players in Chinarsquos coal-mine safety productionsystem

21 Game Design and Description Currently the work be-havior of all employees in the coal-mine enterprise deter-mines the status of coal-mine safety production Here thesafety production system is defined relative to the safetysupervision system e current game system of coal-minesafety supervision is the game between the companyrsquos ex-ternal regulators (including national regulators and localsafety regulators) and the coal mining enterprises them-selves however the safety production system refers to thegame among the participants in the internal safety man-agement system of coal-mine enterprise e stakeholders incoal-mine safety production system include the organiza-tion the first-line miners and the first-line managers

Among them the organization refers to the senior managersof coal-mine enterprises and their main duties includeformulating reasonable reward punishment measures andsafety management decisions the first-line miners representthe employees who carry out front-line operations whoseunsafe behavior most directly leads to accidents and thefirst-line managers are safety supervision departmentswhich mainly supervise the daily safety of coal minerserefore the work behavior includes the senior regulationof the organization the safe operation of the miners and thegrass-root supervision of the mangers e systemicallyevolutionary game of these stakeholders in the coal-minesafety production is developed and studied

According to the Regulations of Coal Mining SafetyManagement the organization is responsible for protectingcoal enterprisesrsquo production situation by the incentivestrategy To represent their incentive strategy in the evo-lutionary game model we designated x (0le xle 1) as theincentive ratio of the organization When x= 0 or x= 1 itrepresents general incentive or positive incentive Further-more the decisions about the incentive strategy have costimplications e positive incentive cost is high so limitedincentive level is practical During the process of coalmining r1 represents the profits from positive incentive andc1 represents the safety investment cost of positive incentiveIf the organization chooses general incentive it will save thesafety investment cost but may increase the accidentprobability and then result in an expected loss later on andthe cost which organization adopts general incentive is c2c1 lt c2 and the profit is r2

e miners choose y (0le yle 1) as their strategy in theiroperation process in which y represents safety operationratio When y 0 or y 1 it represents unsafe operation andsafe operation respectively During the process of coalmining t1 represents the safety performance of safe oper-ation t2 represents the safety rewards of safe operationunder positive incentives t3 represents the safety rewards ofsafe operation under general incentives and c3 representsthe safe operation cost If the miners choose unsafe oper-ation it will save the cost and gain physical and mentalbenefits but may increase the accident probability and thenresult in an expected punishment loss later on During thisprocess t4 represents the physical and mental profits t5represents the safety performance of unsafe operation c4represents the unsafe operation cost c5 represents the finewhen the unsafe behavior of miner are supervised and re-ported by the manager and c6 represents the bribe cost ofminer paying to the manager

e managers choose z (0le zle 1) as their strategy whensupervising the miners in which z represents supervisionratio of the managers When z 0 it represents the dere-liction supervision duty and even power rent seeking andz 1 represents strict execution of supervision dutiesDuring the process of supervising s1 represents the partialldquocommissionrdquo profits from fines for their safety supervisionwork s3 represents the safety performance of safety su-pervision s5 represents the safety rewards of safety super-vision under positive incentives s6 represents the safetyrewards of safety supervision under general incentives and

Complexity 3

c7 represents the safety supervision cost If the managerschoose dereliction of supervision duty and even power rentseeking they will gain rents from miners but also undertakeexpected loss later at the same time During this rent-seekingprocess s2 represents the ldquobriberdquo profits s4 represents thesafety performance of rent seeking s4 lt s3 and c7 representsthe rent-seeking cost

e above variables are shown in Table 1 Furthermorethe payoff matrix among the organization miners andmanagers is shown in Table 2 according to above precedingassumption and analysis

22 Game Solution According to the evolutionary gametheory replicator dynamics is used to represent the learningand evolution mechanism of individuals in the process ofcoal-mine safety production erefore the organizationrsquospositive incentive fitness and general incentive fitness can beobtained as follows based on the above analysis and Table 2

Ux z y r1 minus c1( 1113857 +(1 minus y) r1 minus c2 + c5 minus s1( 11138571113858 1113859

+(1 minus z) y r1 minus c1( 1113857 +(1 minus y) r1 minus c1( 11138571113858 1113859

yz s1 minus s5( 1113857 + z c5 minus s1( 1113857 + r1 minus c1

(1)

U1minus x z y r2 minus c2( 1113857 +(1 minus y) r2 minus c2 + c5 minus s3 minus s1( 11138571113858 1113859


yz s1 + s3 minus c5( 1113857 + z c5 minus s3 minus s1( 1113857 + r2 minus c2

(2)

where Ux represents positive incentive fitness and U1minus x

represents general incentive fitnessus average fitness of the organization can be obtained

as follows

Ux1minus x xUx +(1 minus x)U1minus x (3)

According to the replicator dynamics the change rate ofx is as follows

dx

dt x Ux minus Ux1minus x1113872 1113873 x Ux minus xUx +(1 minus x)U1minus x( 1113857( 1113857

x(1 minus x) Ux minus U1minus x( 1113857

(4)

Let F(x y z) (dxdt) and substitute equations (1) and(2) into equation (4) and then get equation (5) as followsnamely organizationrsquos replicated dynamic equation

F(x y z) x(1 minus x) yz s1 minus s5( 1113857 + z c5 minus s1( 1113857 + r1 minus c11113858 11138591113864

minus yz s1 + s3 minus c5( 1113857 + z c5 minus s3 minus s1( 1113857 + r2 minus c21113858 11138591113865

(5)

Similarly the change rate of y and z are as follows

G(x y z) dy

dt y Uy minus U1minus y1113872 1113873 y(1 minus y) xz t2 minus t3( 11138571113858

+ z t3 minus t5 + t1 + c5 minus c6( 1113857 minus c3 minus t4 + c4 + c61113859

H(x y z) dz

dt z Uz minus U1minus z( 1113857 z(1 minus z) xy s5 minus s6( 11138571113858

+ y s6 minus s1 minus s3 + s4 + s2 minus c7( 1113857

+ s1 + s3 minus s2 minus s41113859

(6)

In conclusion the population dynamic of the evolu-tionary game in the coal mining safety production can berepresented by the following replicated dynamic equationset

F(x y z) dx

dt x Ux minus U1minus x( 1113857 x(1 minus x) minus yzs3 + zs3 + r1 minus c1 minus r2 + c2( 1113857

G(x y z) dy

dt y Uy minus U1minus y1113872 1113873 y(1 minus y) xz t2 minus t3( 1113857 + z t3 minus t5 + t1 + c5 minus c6( 1113857 minus c3 minus t4 + c4 + c61113858 1113859

H(x y z) dz

dt z Uz minus U1minus z( 1113857 z(1 minus z) xy s5 minus s6( 1113857 + y s6 minus s1 minus s3 + s4 + s2 minus c7( 1113857 + s1 + s3 minus s2 minus s41113858 1113859

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)

e above replicated dynamic equation set equation (7)reflects the speed and direction of the strategy adjustmentamong the organization miners and managers When it isequal to zero it shows that the speed of strategy adjustmentis equal to zero and the evolutionary game system reaches arelatively stable equilibrium state Furthermore the stabilityof equilibrium solution can be obtained by analyzing theJacobian matrixrsquos determinant [40ndash43] and trace of the

game which reflects the existence of the evolutionary stablestrategy

23 Stability Analysis of the Evolutionary Game ModelAccording to the replication dynamic equations of the or-ganization miners and managers the eight equilibriumpoints of the dynamic games are E1 (0 0 0) E2 (0 0 1) E3 (0

4 Complexity

1 0) E4 (0 1 1) E5 (1 0 0) E6 (1 0 1) E7 (1 1 0) and E8 (11 1) respectively e Jacobian matrix of the dynamic gameof the organization miners and managers is shown in thefollowing equation

J

zF(x y z)

zx

zF(x y z)

zy

zF(x y z)

zz

zG(x y z)

zx

zG(x y z)

zy

zG(x y z)

zz

zH(x y z)

zx

zH(x y z)

zy

zH(x y z)

zz

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

B1 B2 B3

B4 B5 B6

B7 B8 B9

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where

B1 (1 minus 2x) minus yzs3 + zs3 + r1 minus c1 minus r2 + c2( 1113857

B2 minus xz(1 minus x)s3

B3 x(1 minus x)(1 minus y)s3

B4 yz(1 minus y) t2 minus t3( 1113857

B5 (1 minus 2y) xz t2 minus t3( 1113857 + z t3 minus t5 + t1 + c5 minus c6( 11138571113858

minus c3 minus t4 + c4 + c61113859

B6 y(1 minus y) x t2 minus t3( 1113857 + t3 minus t5 + t1 + c5 minus c61113858 1113859

B7 yz(1 minus z) s5 minus s6( 1113857

B8 z(1 minus z) x s5 minus s6( 1113857 + s6 minus s1 minus s3 + s4 + s2 minus c71113858 1113859

B9 (1 minus 2z) xy s5 minus s6( 1113857 + y s6 minus s1 minus s3 + s4 + s2 minus c7( 11138571113858


(9)

From the local stability of the Jacobian matrix it can beseen that when the equilibrium point is brought into thematrix J to satisfy both the determinant DetJgt 0 and the traceTrJgt 0 the equilibrium point is an evolutionary stabilitystrategy and the decision-making agent reaches the evo-lutionary stability strategy (ESS) if the determinant DetJgt 0and the trace TrJgt 0 the equilibrium point is unstable if thedeterminant DetJlt 0 and the trace TrJ 0 or is indetermi-nate the equilibrium point is a saddle point e stabilityanalysis results of the above eight equilibrium points are asfollows

(1) e condition that the equilibrium point E1 (0 0 0)is satisfied as the stable equilibrium point isr1 minus c1 minus r2 + c2 lt 0 c3 + t4 minus c4 minus c6 lt 0 s1 + s3 minus s2minus s4 lt 0 Under this condition we find that the unsafeoperation cost of miners is greater than the profits ofthe unsafe operation Obviously the miners willchange their initial strategy which contradicts theequilibrium point So the equilibrium point E1 (0 00) is not an evolutionary stability strategy

(2) e condition that the equilibrium point E2 (0 0 1)is satisfied as the stable equilibrium point iss3 + r1 minus c1 minus r2 + c2 lt 0 t1 + t3 minus t4 minus t5 + c4 + c5 minus

c3 lt 0 s2 + s4 minus s1 minus s3 lt 0 Under this condition wefind that the profits of safety supervision of managersare less than the profits of rent seeking Obviouslythe managers will choose power rent-seeking strat-egies which contradicts the equilibrium points sothe equilibrium point E2 (0 0 1) is not an evolu-tionary stabilization strategy

(3) e condition that the equilibrium point E3 (0 1 0)is satisfied as the stable equilibrium point isr1 minus c1 minus r2 + c2 lt 0 c3 + t4 minus c4 minus c6 lt 0 s6 minus c7 lt 0However this condition of s6 minus c7 lt 0 cannot judgethe relationship between the safety regulation costand the profits so the equilibrium point E3(0 1 0) isnot an evolutionary stabilization strategy

Table 1 Variables in the game among the organization minersand managers

Variables Meaning of the variables Notesx Incentive ratio 0le xle 1y Safe operation ratio 0le yle 1z Safety supervision ratio 0le zle 1r1 Positive incentive profits of organization r1 gt 0c1 Positive incentive cost of organization c1 gt c2r2 General incentive profits of organization r2 gt 0c2 General incentive cost of organization c2 gt 0

t1Safety performance of safe operation of

miners t1 gt t5

t2Safety rewards of safe operation of miners

under positive incentives t2 gt t3


under general incentives t3 gt 0

c3 Safe operation cost of miners c3 gt 0

t4Physical and mental profits of unsafe

operation of miners t4 gt 0

t5Safety performance of unsafe operation of

miners t5 gt 0

c4 Unsafe operation cost of miners c4 gt 0c5 e fine of unsafe operation of miners c5 gt 0

c6e bribe cost of miner paying to the

manager c6 gt 0

s1e ldquocommissionrdquo profits from fines for

managerrsquos safety supervision s1 gt 0

s3Safety performance of safety supervision of

managers s3 gt s4

s5Safety rewards of safety supervision ofmanagers under positive incentives s5 gt s6

s6Safety rewards of safety supervision ofmanagers under general incentives s6 gt 0

c7Safety supervision cost or rent-seeking cost

of managers c7 gt 0

s2 e ldquobriberdquo profits of managers s2 gt 0

s4Safety performance of rent-seeking of

managers s4 gt 0

Complexity 5

(4) e condition that the equilibrium point E4 (0 1 1)is satisfied as the stable equilibrium point isr1 minus c1 minus r2 + c2 lt 0 t4 + t5 minus t1 minus t3 minus c4 minus c5 +

c3 lt 0 c7 minus s6 lt 0 Under this condition the netprofits of organizationrsquos positive incentive are lessthan the net profits of the general incentive so theorganization will adopt the general incentive strat-egy the net profits of the minersrsquo unsafe operationare less than the net profits of safe operation so theminer will take safe operation the incentives forsafety supervision are greater than the costs so themanagers will choose safety supervision strategyerefore if the conditions of the evolutionarystability strategy are satisfied the evolutionary sta-bility strategy of the organization miners andmanagers will eventually evolve into general in-centive safe operation and safety supervisionwhich indicates that the equilibrium point E4 (0 1 1)is an evolutionary stabilization strategy

(5) e condition that the equilibrium point E5 (1 0 0)is satisfied as the stable equilibrium point isc1 minus r1 + r2 minus c2 lt 0 c3 + t4 minus c4 minus c6 lt 0 s1 + s3 minus s2minus s4 lt 0 Under this condition we find that theunsafe operation cost of miners is greater than theprofits of the unsafe operation Obviously theminers will change their initial strategy whichcontradicts the equilibrium point so the equilib-rium point E5 (1 0 0) is not an evolutionary sta-bility strategy

(6) e condition that the equilibrium point E6 (1 0 1)is satisfied as the stable equilibrium point isc1 minus r1 + r2 minus c2 minus s3 lt 0 t1 + t2 minus c3 minus t4 minus t5 + c4 +

c5 lt 0 s2 + s4 minus s1 minus s3 lt 0 Under this condition wefind that the profits of safety supervision of man-agers are less than the profits of rent-seekingObviously the managers will choose power rent-seeking strategies which contradicts the equilib-rium points so the equilibrium point E6 (1 0 1) isnot an evolutionary stabilization strategy

(7) e condition that the equilibrium point E7 (1 1 0) issatisfied as the stable equilibrium point is

c1 minus r1 + r2 minus c2 lt 0 c3 + t4 minus c4 minus c6 lt 0 s5 minus c7 lt 0Under this condition the net profits of organiza-tionrsquos positive incentive are greater than the netprofits of the general incentive so the organizationwill adopt the positive incentive strategy the netprofits of the unsafe operation are less than the netprofits of safe operation so the miner will take safeoperation the safety supervision cost of managers isgreater than the profits so the managers will chooseno supervision strategy or even rent-seeking strategyerefore if the conditions of the evolutionarystability strategy are satisfied the evolutionary sta-bility strategy of the organization miners andmanagers will eventually evolve into positive in-centive safe operation and no supervision or evenrent-seeking strategy which indicates that theequilibrium point E7 (1 1 0) is an evolutionarystabilization strategy

(8) e condition that the equilibrium point E8 (1 1 1) issatisfied as the stable equilibrium point isc1 minus r1 + r2 minus c2 lt 0 t4 + t5 minus t1 minus t2 minus c4 minus c5 + c3lt 0 c7 minus s5 lt 0 Under this condition the net profitsof organizationrsquos positive incentive are greater thanthe net profits of the general incentive so the or-ganization will adopt the positive incentive strategythe net profits of the unsafe operation are less thanthe net profits of safe operation so the miner willtake safe operation the safety supervision cost ofmanagers is less than the profits so the managers willchoose safety supervision erefore if the condi-tions of the evolutionary stability strategy are sat-isfied the evolutionary stability strategy of theorganization miners and managers will eventuallyevolve into positive incentive safety operation andsafety supervision which indicates that the equi-librium point E8 (1 1 1) is an evolutionary stabi-lization strategy

From the stability analysis of the eight equilibriumpoints we find that E4 (0 1 1) E7 (1 1 0) and E8 (1 1 1) areevolutionary stability strategies of the organization minersand managers

Table 2 Payoff matrix of the three-party game

MinerSafe operation Unsafe operation

Organization

Positive incentiver1 minus c1 r1 minus c1 + c5 minus s1

Safety supervision

Manager

t1 + t2 minus c3 t4 + t5 minus c4 minus c5s3 + s5 minus c7 s1 + s3 minus c7

General incentiver2 minus c2 r2 minus c2 + c5 minus s3 minus s1


Positive incentiver1 minus c1 r1 minus c1

No supervision or even power rent seeking

t1 minus c3 t1 + t4 minus c4 minus c6s3 s2 + s4 minus c7

General incentiver2 minus c2 r2 minus c2t1 minus c3 t1 + t4 minus c4 minus c6

s3 s2 + s4 minus c7

6 Complexity

3 Simulation Analysis of the EvolutionaryGame Model

Matlab simulation technology is an effective computer sim-ulation method for studying feedback behavior in complexsystems [44ndash49] In the above multiplayer game the indi-viduals constantly imitate and learn from other individuals byobserving and comparing the payoffs with others and thenadjust their strategy selection which constitutes the feedbackbehavior in the group erefore this section will first use theMatlab simulation technology to verify the above threeequilibrium points and then provide an effective simulationplatform to determine reasonable regulation strategies

31 Numerical Simulations of the Stable Equilibrium PointIn order to more intuitively show the evolution path of thesystem the above evolutionary game equilibrium points areanalyzed and verified by numerical simulation

In order to make the system finally evolve to the idealstate point E4 (0 1 1) the initial values of each parameterneed to meet the following conditions r1 minus c1 minus r2 + c2 lt 0t4 + t5 minus t1 minus t3 minus c4 minus c5 + c3 lt 0 and c7 minus s6 lt 0 and theinitial values are set as c1 15 r1 15 c2 11 r2 13 s3 2t1 3 t2 3 t3 2 t4 6 t5 1 c3 4 c4 3 c5 4 c6 3s1 3 s2 3 s4 1 s5 7 s6 6 and c7 5

Under the above conditions the initial value of x is fixedand the initial values of y and z are randomly selected toverify the influence of the initial values of y and z on thechange of x with time Taking x 05 as an example theevolution curve of x is as shown in Figure 1(a) It can be seenfrom Figure 1(a) that the difference of the initial values of yand z affect the convergence speed of x but x still mono-tonically decreases and converges to 0 indicating that theproportion of the organization selecting the ldquopositive in-centiverdquo strategy will continue to decrease over time andultimately all will choose the ldquogeneral incentiverdquo strategyregardless of the initial values of y and z Taking z 05 as anexample the values of x and y are varied to obtain theevolution curve of z as shown in Figure 1(c) As can be seenin Figure 1(c) the difference of the initial values of x and yaffect the convergence speed of z but z still monotonicallyincreases and converges to 1 indicating that the proportionof managers choosing ldquosafety supervisionrdquo strategy willcontinue to increase over time and ultimately all will choosethe ldquosafety supervisionrdquo strategy regardless of the initialvalues of x and y Taking y 05 as an example the values of xand z are varied to obtain the evolution curve of y as shownin Figure 1(b) However when the initial proportion of theorganization adopting the ldquopositive incentiverdquo strategy andthe managers adopting the ldquosafety supervisionrdquo strategy isgreater than 07 the miners will finally choose the safeoperation otherwise the miners will eventually choose theunsafe operation which is inconsistent with the stability ofthe equilibrium point E4 (0 1 1) erefore the equilibriumpoint E4 (0 1 1) is not an ideal steady state

In order to make the system finally evolve to the idealstate point E7 (1 1 0) the initial values of each parameterneed to meet the following conditions c1 minus r1 + r2 minus c2 lt 0

c3 + t4 minus c4 minus c6 lt 0 and s5 minus c7 lt 0 and the initial values areset as c1 3 r1 4 c2 2 r2 2 s3 4 t1 2 t2 2 t3 1t4 3 t5 1 c3 4 c4 3 c5 6 c6 5 s4 3 s5 2 s6 1and c7 3

Similarly under the above conditions the evolutioncurves of x y and z are shown in Figures 2(a)ndash2(c) re-spectively It can be seen from Figure 2(a) that the dif-ference of the initial values of y and z affect theconvergence speed of x but x still monotonically increasesand converges to 1 indicating that the proportion of theorganization selecting the ldquopositive incentiverdquo strategy willcontinue to increase over time and ultimately all willchoose the ldquopositive incentiverdquo strategy regardless of theinitial values of y and z It can be seen from Figure 2(b) thatthe difference of the initial values of x and z has an effect onthe convergence speed of y but y still monotonically in-creases and converges to 1 indicating that the proportionof miners choosing the ldquosafe operationrdquo strategy willcontinue to increase over time and eventually all choosethe ldquosafe operationrdquo strategy regardless of the initial valuesof x and z As shown in Figure 2(c) however it is foundthat managers will abandon safety supervision when theinitial probability of the organization adopting ldquopositiveincentiverdquo strategy and the miners adopting ldquosafe opera-tionrdquo strategy is large while the managers will choosesafety regulation when the initial probability of the or-ganization adopting ldquopositive incentiverdquo strategy and theminers adopting ldquosafe operationrdquo strategy is small which isinconsistent with the stability of the equilibrium point E7(1 1 0) erefore the equilibrium point E7 (1 1 0) is notan ideal steady state

In order to make the system finally evolve to the idealstate point E8 (1 1 1) the initial values of each parameterneed to meet the following conditions c1 minus r1 + r2 minus c2 lt 0t4 + t5 minus t1 minus t2 minus c4 minus c5 + c3 lt 0 and c7 minus s5 lt 0 and theinitial values are set as c1 18 r1 20 c2 17 r2 18 s3 6t1 3 t2 3 t3 2 t4 4 t5 2 c3 6 c4 4 c5 7 c6 6s1 3 s2 3 s4 1 s5 6 s6 5 and c7 5

Similarly under the above conditions the evolutioncurves of x y and z are shown in Figures 3(a)ndash3(c) re-spectively It can be seen from Figure 3(a) that the differenceof the initial values of y and z affects the convergence speedof x but x still monotonically increases and converges to 1indicating that the proportion of the organization selectingldquopositive incentiverdquo strategy will continue to increase overtime and ultimately all will choose the ldquopositive incentiverdquostrategy It can be seen from Figure 3(b) that the difference ofthe initial values of x and z has an effect on the convergencespeed of y but y still monotonically increases and convergesto 1 indicating that the proportion of miners choosing theldquosafe operationrdquo strategy will continue to increase over timeand eventually all will choose the ldquosafe operationrdquo strategyAs can be seen in Figure 3(c) the difference of the initialvalues of x and y affects the convergence speed of z but z stillmonotonically increases and converges to 1 indicating thatthe proportion of managers choosing ldquosafety supervisionrdquostrategy will continue to increase over time and eventually allwill choose the ldquosafety supervisionrdquo strategy is is con-sistent with the stability of the equilibrium point E8 (1 1 1)

Complexity 7

so the equilibrium point E8 (1 1 1) is the unique ideal steadystate

It can be seen from Figure 3 that when the initialproportion of a game agent is determined the change of theinitial proportion of the other two agents has no effect on itsfinal strategy choice In order to more accurately describe themutual influence of the three-party game the initial pro-portion of the organization is set to x 04 the initialproportion of the miners is set to y 05 and the initialproportion of the managers is set to z 06 and the

evolution curves of x y and z are shown inFigures 4(a)ndash4(c) respectively

As shown in Figure 4 when the net profits of organi-zationrsquos positive incentive are greater than the net profits ofthe general incentive the net profits of the unsafe operationare less than the net profits of safe operation and the safetysupervision cost of managers is less than the profits re-gardless of the initial proportion of x y and z the threeagents will choose the optimal and initial decision and thegreater the initial proportion the shorter the time to reach

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)

Figure 1 (a) Evolution curve of xwhen y and z change (b) Evolution curve of ywhen x and z change (c) Evolution curve of zwhen x and y change

8 Complexity

the optimal strategy and the smaller the initial proportionthe longer the time to reach the optimal strategy

Now taking x 03 y 05 and z 07 as an examplethe evolutionary trend of the organization miners andmanagers is demonstrated as shown in Figure 5 e finalevolution of the three agents is positive incentive safeoperation safety supervision which confirms the stabilityof the equilibrium point E8 (1 1 1) erefore the equi-librium point E8 (1 1 1) is the only ideal steady state

32 Stability of the Dynamical Game System with Incentive-Punishment Strategy In order to make the dynamic gamesystem reach the evolutionary steady state more quicklyunder the stable condition that satisfies the ideal state pointE8 (1 1 1) first we increase the incentives (performance payand bonuses) for the safe operation of miners and the safetysupervision of managers the penalty costs for unsafe op-erations of miners and no supervision and even power rentseeking by managers remain unchanged that is the

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9

parameters are adjusted to c1 22 r1 24 c2 21 r2 22s3 7 t1 4 t2 2 s1 4 and s5 7 and other parametersare unchanged the evolution result of the dynamic gamesystem is shown in Figure 6 In addition we increase thepenalty costs for unsafe operations of miners and no su-pervision and even power rent seeking of managers and theincentives (performance pay and bonuses) for the safe op-eration of miners and the strict supervision of managersremain unchanged that is the parameters are adjusted toc5 9 and s4 0 and other parameters are unchanged the

evolution result of the dynamic game system is shown inFigure 7 Finally we also increase the incentives (perfor-mance pay and bonuses) for the safe operation of miners andthe safety supervision of managers and the penalty costs forunsafe operation of miners and no supervision and evenpower rent seeking of managers that is the parameters areadjusted to c1 22 r1 24 c2 21 r2 22 s3 7 t1 4t2 2 s1 4 s5 7 c5 9 and s4 0 and other parametersare unchanged the evolution result of the dynamic gamesystem is shown in Figure 8

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)

Figure 3 (a) Evolution curve of x when y and z change (b) Evolution curve of y when x and z change (c) Evolution curve of z when x and ychange

10 Complexity

By comparing Figures 5ndash8 it can be found that thedynamic game system needs 5 s to reach a steady state in theinitial setting when only the reward strategy is adopted thesystem can be stabilized in 25 s which can be reduced byhalf when only the penalty strategy is adopted the systemcan be stabilized in 35 s when the reward strategy and thepenalty strategy are adopted at the same time the system canbe stabilized in 2 s e above numerical simulation resultsshow that the combination of positive incentive policies andstrict penalties policies can make the game model reach astable state more quickly

4 Discussion

rough the decision-making dynamic replication analysisevolution stability analysis and numerical simulation ex-periments among the three stakeholders of the organization

miners and managers in coal-mine safety production theresults of this paper include the following three parts

(1) From the dynamic replication equation of the decisionmaking the proportion of decision making of orga-nizationrsquos ldquopositive incentivesrdquo is related to the pro-portion of minersrsquo ldquosafety operationrdquo and theproportion of decision making under managersrsquo safetysupervision the proportion of minersrsquo ldquosafety opera-tionrdquo is related to the proportion of decisionmaking oforganizationrsquos ldquopositive incentivesrdquo and managersrsquosafety supervision the proportion of decision makingunder managersrsquo safety supervision is related to theproportion of organizationrsquos ldquopositive incentivesrdquo andminersrsquo ldquosafety operationrdquo Specifically whether theorganization decides to adopt the positive incentiveswill be directly affected by whether the miner adoptsthe safe operation and whether the manager adopts

y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)

Figure 4 (a)e evolution curve of x when y 05 and z 06 (b)e evolution curve of y when x 04 and z 06 (c)e evolution curveof z when x 04 and y 05

Complexity 11

safety supervision whether the miner decides to adoptthe safe operation decision will be directly affected bywhether the organization adopts the positive incen-tives and whether the manager adopts safety super-vision Whether the manager adopts the decision ofsafety supervision is influenced by whether the or-ganization adopts the positive incentives and whetherminers adopt safe operation e above result showsthat the decision making of organization miners andmanagers interact with each other the bridge amongthe three agents is the managers so the exiting static

analyses of the game between two stakeholders hascertain limitations [31] In the process of coal-minesafety production it is necessary to make clear theinfluence relationship among the three

(2) From the analysis on evolution stability we can seethat these equilibrium points of E1 (0 0 0) E2 (0 01) E5 (1 0 0) and E6 (1 0 1) are not stable stateindicating that if the miners choose unsafe oper-ation no matter what strategy the organization andmanagers adopt the evolutionary game model willnot reach the stable state From the perspective of

xyz

0

03

05

07

1

Pr

30 1 42 5t

Figure 5 e final evolution result of E8 (1 1 1) with the initialsetting

xyz

0

03

05

07

1

Pr

05 15 250 1 2t

Figure 6 e final evolution result of E8 (1 1 1) with incentivestrategy

xyz

05 15 25 3530 1 2t

0

03

05

07

1

PrFigure 7 e final evolution result of E8 (1 1 1) with punishmentstrategy

xyz

0

03

05

07

1

Pr

05 150 21t

Figure 8 e final evolution result of E8 (1 1 1) with incentive-punishment strategy

12 Complexity

evolutionary game it is proved that the unsafebehavior of miners is the most direct and maincause of coal-mine safety accidents [2ndash4] and thedecision making of miners plays an important rolein the operation of coal-mine safety production[29ndash31 50 51] In addition the equilibrium pointE3 (0 1 0) is not stable state Even if the miners takesafe operation at the initial stage they will grad-ually evolve the unsafe operation to alleviate thehigh work stress if the organization has been ingeneral incentive state and the manager has notimplemented strict supervision And in the end theminers tend to gain psychological benefits fromunsafe operation and adopt unsafe operationFurthermore the equilibrium points that can makethe evolutionary game model reach a steady stateare E4 (0 1 1) E7 (1 1 0) and E8 (1 1 1) ismeans that certain positive incentive from orga-nization and certain safety supervision frommanagers are necessary for the miners to adoptsafety operation otherwise the miners lack thedriving force to conduct safety operation eorganization and managers should realize that theincentive type mode and strict supervision forsafety production are effective driving factors forminers to take safe operation

(3) From the numerical simulation results we can seethat only the equilibrium point E8 (1 1 1) is the idealsteady state and when three conditions are satisfiedthe three agents can achieve the ideal state① the netprofits of organizationrsquos positive incentive are greaterthan the net profits of the general incentive ② thenet profits of the unsafe operation are less than thenet profits of safe operation and ③ the safety su-pervision cost of managers is less than the profitse three stakeholders who are the organizationminers and managers can achieve the ideal condi-tion that is the ideal safety production state oforganization adopting positive incentive minersadopting safe operation and managers taking safetysupervision It can be seen that the final evolutionarystate of the game model of the organization minersand managers will depend on the organizationrsquosincentive costs organizational benefits the netprofits of miners incentives and costs for managerstaking safety supervision etc [52] In addition wealso find that the higher the initial proportion of thestrategy portfolio of miners andmanagers the longerthe time of organization converging to a stable idealstate which shows that when the initial proportionof the miners choosing safe operation and themanagers adopting safety supervision is high theorganization will slow down the rate of positiveincentives e higher the initial proportion of thestrategy portfolio of organization and managers theshorter the time of miners converging to a stableideal state which shows that the cooperation be-tween the organization and managers can speed up

the decision-making of the minersrsquo safe operatione higher the initial proportion of the strategyportfolio of organization and miners the longer thetime of managers converging to a stable ideal statewhich shows that when the initial proportion ofminers adopting safe operation and organizationadopting positive incentives is high the managerswill relax the safety supervision for the miners eresults of this numerical simulation reflect an un-reasonable game between the players inside the coal-mine safety production system which is a problemthat we need to pay attention to and improveFurthermore the strategy portfolio with a relativelyhigh initial proportion of three agents convergesmore quickly to an ideal state than a relatively lowstrategy portfolio Finally we find that the combi-nation of positive incentive policies and strict pen-alties policies can make the game model reach astable state more quickly [28] In summary thisstudy shows that the efficient cooperation among theorganization (positive incentives) miners (safe op-eration) and managers (safety supervision) canmake the coal-mine safety production systemquickly enter the ideal state of stable and safeoperation

5 Conclusions

rough the evolution analysis on the decision-makingbehavior of three stakeholders namely the organizationminers and managers it is concluded that the incentive costand net profits of organization supervision costs and profitsof managers and net profits of miners are crucial factors toachieve the ideal decision making of stakeholders and thecombination of positive incentive policies and strict pun-ishment policies are the key to ensuring that the game modelquickly reaches a stable state the conclusions are as follows

(1) As the senior manager of coal mining enterprise theorganization can appropriately improve the level ofsafety incentives and formulate reward and pun-ishment mechanisms and provide reasonable eco-nomic and policy support for safety production sothat enterprises can realize the transition from thepenalty type management mode for safety produc-tion to the incentive-punishment management modefor safety production For the organization super-vision scientific methods shall be adopted to pro-mote the efficiency of safety production When boththe miners and managers adopt safe strategy or-ganizations should make more rewards rather thanreduce rewards At the same time it shall be realizedthat the deterrent effect will decline in case of blindlyintensifying supervision and penalty and the gameamong the organization miners and managers willbe more seriouse organization can adopt market-oriented means with the stimulation of economicinterests publicity guidance and policy support soas to enable the coal mining enterprises to internalize

Complexity 13

the goal of improving the safety production eorganization and managers can use effective safetyeducation to raise minersrsquo awareness and enthusiasmfor safety production and create a good climate forsafety production e expression mechanism of theminersrsquo interests should be provided to ensure theexpression of minersrsquo interests and psychologicalappeals and enable miners to positively and effec-tively communicate with managers such asstrengthening the construction of trade unions andproviding specialized mental health and safetycounseling offices to communicate and guide on thepsychological pressures of miners

(2) As the most direct supervisor of first-line minersthe managers should strengthen the safety super-vision of minersrsquo production operations regardlessof whether miners choose safe operation or unsafeoperation they should strengthen supervision ofminers and they should promote the safety climateof the group through cultural driving and thenpromote the minersrsquo deep sense of safety awarenessand compliance practices Managers shouldstrengthen the safety culture in the group andcreate safety responsibility beliefs of team safetyresponsibility mentality and safety responsibilitybehaviors of team Furthermore managers canprovide counseling and education for the ldquore-sponsibilityrdquo of miners such as holding speechesand photography competitions related to safetyresponsibility In this way the awareness of thesafety behavior of miners is increased and thepossibility of violations is reduced

(3) Miners are the direct executor of coal-mine pro-duction and play a key role in avoiding safety ac-cidents In order to positively respond to the safetyattention of organizations and managers and tobetter protect their own safety and the expression oftheir own interests the miners should not onlystrengthen their own safety awareness and safetyattitude and choose safe operation in their work butalso form a positive and habitual awareness of rightsprotection When individuals face greater workstress or psychological pressure they should posi-tively communicate with managers and organiza-tional departments in order to get help from themand thus relieve stress and work safe instead ofventing emotions through unsafe operation Whenpersonal interests are infringed they should posi-tively report to the trade unions and properly andeffectively protect their rights through legal channelsrather than blindly solving problems

In the study the decision-making behavior evolutionpath and evolution law of three stakeholders of organizationminers andmanagers are revealed and the stable conditionsfor the main decision to reach the ideal state are found oute simulation is carried out to provide theoretical referenceand practical guidance for the organization safety incentive

mode miner safety operation strategy and manager safetysupervision decision making Next the research will focuson the tetragonal evolutionary game of organization groupminers and managers combined with the classic paradigmof cognitive neuroscience using event-related potentialtechnology the research will focus on further experimentverification of the evolution of the decision-making behaviorof the organization group miners and managers to makethe verification process and result more objective scientificand referential

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

Yan Li and Yan Zhang are the co-first authors ey con-tributed equally to this paper

Acknowledgments

is work was financially supported by the National NaturalScience Foundation of China (Grant no 51604216) andPhilosophy and Social Science Prosperity Project of XirsquoanUniversity of Science and Technology (Grant no 2018SZ04)e authors wish to acknowledge the crucial role of col-laborating coal companies participants members of ourresearch teams and all stakeholders involved in the datacollection and supporting tasks

References

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[2] S S Chen J H Xu and Y Fan ldquoHow to improve the reg-ulatory performance of the provincial administrations of coalmine safety in China a grey clustering assessment based oncentre-point mixed triangular whitenisation weight functionrdquoInternational Journal of Global Energy Issues vol 39 no 6pp 367ndash381 2016

[3] M F Ullah A M Alamri K Mehmood et al ldquoCoal miningtrends approaches and safety hazards a brief reviewrdquoArabian Journal of Geosciences vol 11 no 21 p 651 2018

[4] C Wang J Wang X Wang H Yu L Bai and Q SunldquoExploring the impacts of factors contributing to unsafebehavior of coal minersrdquo Safety Science vol 115 pp 339ndash3482019

[5] R Tong Y Zhang P Cui C Zhai M Shi and S XuldquoCharacteristic analysis of unsafe behavior by coal minersmulti-dimensional description of the pan-scene datardquo In-ternational Journal of Environmental Research and PublicHealth vol 15 no 8 p 1608 2018

14 Complexity

[6] L F Fang Z X Zhang and H H Guo ldquoCognitive mech-anism and intervention strategies of coal minersrsquo unsafebehaviors evidence from Chinardquo Revista DE Cercetare SIInterventie Sociala vol 61 pp 7ndash31 2018

[7] A C Joaquim M Lopes L Stangherlin et al ldquoMental healthin underground coal minersrdquo Archives of Environmental andOccupational Health vol 73 no 6 pp 334ndash343 2018

[8] X Wu W Yin C Wu and Y Li ldquoDevelopment and vali-dation of a safety attitude scale for coal miners in ChinardquoSustainability vol 9 no 12 p 2165 2017

[9] J-Z Li Y-P Zhang X-J Wang et al ldquoRelationship researchbetween subjective well-being and unsafe behavior of coalminersrdquo Eurasia Journal of Mathematics Science and Tech-nology Education vol 13 no 11 pp 7215ndash7221 2017

[10] E J Haas B Eiter C Hoebbel and M E Ryan ldquoe impactof job site and industry experience on worker health andsafetyrdquo Safety vol 5 no 1 p 16 2019

[11] S Han H Chen E Stemn and J Owen ldquoInteractions be-tween organisational roles and environmental hazards thecase of safety in the Chinese coal industryrdquo Resources Policyvol 60 pp 36ndash46 2019

[12] J A Dobson D L Riddiford-harland A F Bell andJ R Steele ldquoEffect of work boot type on work footwear habitslower limb pain and perceptions of work boot fit and comfortin underground coal minersrdquo Applied Ergonomics vol 60pp 146ndash153 2017

[13] Q Cao K Yu L Zhou LWang and C Li ldquoIn-depth researchon qualitative simulation of coal minersrsquo group safety be-haviorsrdquo Safety Science vol 113 pp 210ndash232 2019

[14] M M Aliabadi H Aghaei O Kalatpour A R Soltanian andM Seyedtabib ldquoEffects of human and organizational defi-ciencies on workersrsquo safety behavior at a mining site in IranrdquoEpidemiology and Health vol 40 Article ID e2018019 2018

[15] E J Haas and P L Yorio ldquoe role of risk avoidance andlocus of control in workersrsquo near miss experiences implica-tions for improving safety management systemsrdquo Journal ofLoss Prevention in the Process Industries vol 59 pp 91ndash992019

[16] J M Beus S C Payne W Arthur and G J Muntildeoz ldquoedevelopment and validation of a cross-industry safety climatemeasure resolving conceptual and operational issuesrdquoJournal of Management vol 45 no 5 pp 1987ndash2013 2019

[17] M T Newaz P R Davis M Jefferies and M Pillay ldquoVal-idation of an agent-specific safety climate model for con-structionrdquo Engineering Construction and ArchitecturalManagement vol 26 no 3 pp 462ndash478 2019

[18] S Kanwal A H Pitafi A Pitafi M A Nadeem A Younisand R Chong ldquoChina-Pakistan Economic Corridor (CPEC)development projects and entrepreneurial potential of localsrdquoJournal of Public Affairs vol 19 no 4 2019

[19] H-W Kim A Kankanhalli and S-H Lee ldquoExamining giftingthrough social network services a social exchange theoryperspectiverdquo Information Systems Research vol 29 no 4pp 805ndash828 2018

[20] M Madanoglu ldquoeories of economic and social exchange inentrepreneurial partnerships an agenda for future researchrdquoInternational Entrepreneurship and Management Journalvol 14 no 3 pp 649ndash656 2018

[21] Q T Fu and T H Zhang ldquoDecision-making research on theminersrsquo unsafe behavior from the perpective of behavioraleconomicsrdquo Modern Mining vol 11 pp 1ndash6 2014

[22] MMirzaei Aliabadi H Aghaei O Kalatpour A R Soltanianand A Nikravesh ldquoAnalysis of human and organizationalfactors that influence mining accidents based on Bayesian

networkrdquo International Journal of Occupational Safety andErgonomics vol 24 pp 1ndash8 2018

[23] MMirzaei Aliabadi H Aghaei O Kalatpour A R Soltanianand M SeyedTabib ldquoEffects of human and organizationaldeficiencies on workersrsquo safety behavior at a mining site inIranrdquo Epidemiology and Health vol 40 Article ID e20180192018

[24] J T Cholz ldquoCooperative regulatory enforcement and politicsof administrative effectivenessrdquo American Political ScienceReview vol 85 no 1 pp 115ndash136 1991

[25] W K Wang Q L Cao and Q Yang ldquoResearch on theenterprises technological innovation investment managementand government subsidizing gamerdquo Soft Science vol 28pp 42ndash46 2014

[26] H F Li and H Gao ldquoGame analysis of coal mine safetyproduction in Chinardquo Coal Economic Research vol 7pp 72ndash75 2004

[27] X Q Zhou and X Q Zou ldquoGame analysis on the safetyproduction inspection of coal mine enterpriserdquo China MiningManagement vol 14 pp 10ndash13 2005

[28] Q Liu X Li and X Meng ldquoEffectiveness research on themulti-player evolutionary game of coal-mine safety regulationin China based on system dynamicsrdquo Safety Science vol 111pp 224ndash233 2019

[29] R W Lu X H Wang Y Hao and L Dan ldquoMultipartyevolutionary game model in coal mine safety managementand its applicationrdquo Complexity vol 2018 Article ID9620142 10 pages 2018

[30] T Yun Y QWang J L Wang and L L Zhang ldquoResearch ondecision-making behavior evolution of government coalmine enterprises and employees under safe educationrdquoEurasia Journal of Mathematics Science and Technology Ed-ucation vol 13 no 12 pp 8267ndash8281 2017

[31] Y Kai L J Zhou Q G Cao and L Zhen ldquoEvolutionary gameresearch on symmetry of workersrsquo behavior in coal mineenterprisesrdquo Symmetry vol 11 no 2 p 156 2019

[32] X Su H L Liu and S Q Hou ldquoe trilateral evolutionarygame of agri-food quality in farmer-supermarket directpurchase a simulation approachrdquo Complexity vol 2018Article ID 5185497 11 pages 2018

[33] L Cheng and T Yu ldquoNash equilibrium-based asymptoticstability analysis of multi-group Asymmetric evolutionarygames in typical scenario of electricity marketrdquo IEEE Accessvol 6 pp 32064ndash32086 2018

[34] X Su S S Duan S B Guo and H L Liu ldquoEvolutionarygames in the agricultural product quality and safety infor-mation system a multiagent simulation approachrdquo Com-plexity vol 2018 Article ID 7684185 13 pages 2018

[35] K Li W Wang Y D T Zheng J Guo and J Guo ldquoGamemodelling and strategy research on the system dynamics-based quadruplicate evolution for high-speed railway oper-ational safety supervision systemrdquo Sustainability vol 11no 5 p 1300 2019

[36] Y Yang and W Yang ldquoDoes whistleblowing work for airpollution control in China A study based on three-partyevolutionary game model under incomplete informationrdquoSustainability vol 11 no 2 p 324 2019

[37] Y Ding L Ma Y Zhang and D Feng ldquoAnalysis of evolutionmechanism and optimal reward-penalty mechanism forcollection strategies in reverse supply chains the case of wastemobile phones in Chinardquo Sustainability vol 10 no 12p 4744 2018

[38] L B V Alves and L H A Monteiro ldquoA spatial evolutionaryversion of the ultimatum game as a toy model of income

Complexity 15

distributionrdquo Communications in Nonlinear Science andNumerical Simulation vol 76 pp 132ndash137 2019

[39] S Shibasaki ldquoe evolutionary game of interspecific mutu-alism in the multi-species modelrdquo Journal of =eoretical Bi-ology vol 471 pp 51ndash58 2019

[40] J G Pope V Bartolino N Kulatska et al ldquoComparing thesteady state results of a range of multispecies models betweenand across geographical areas by the use of the jacobianmatrix of yield on fishing mortality raterdquo Fisheries Researchvol 209 pp 259ndash270 2019

[41] N J Curtis K E Niemeyer and C-J Sung ldquoUsing SIMD andSIMT vectorization to evaluate sparse chemical kinetic Ja-cobian matrices and thermochemical source termsrdquo Com-bustion and Flame vol 198 pp 186ndash204 2018

[42] J Galeski ldquoBesicovitch-Federer projection theorem forcontinuously differentiable mappings having constant rank ofthe Jacobian matrixrdquo Mathematische Zeitschrift vol 289no 3-4 pp 995ndash1010 2018

[43] M A Hansen and J C Sutherland ldquoOn the consistency ofstate vectors and Jacobian matricesrdquo Combustion and Flamevol 193 pp 257ndash271 2018

[44] R Arora S C Kaushik R Kumar and R Arora ldquoSoftcomputing based multi-objective optimization of Braytoncycle power plant with isothermal heat addition using evo-lutionary algorithm and decision makingrdquo Applied SoftComputing vol 46 pp 267ndash283 2016

[45] A Hafezalkotob S Borhani and S Zamani ldquoDevelopment ofa Cournot-oligopoly model for competition of multi-productsupply chains under government supervisionrdquo Scientia Ira-nica vol 24 no 3 pp 1519ndash1532 2017

[46] S H Li X J Lv and W G Zhang ldquoGrey dynamic gamebetween the government and auto enterprises for energysaving and emission reductionrdquo Journal of Grey Systemvol 27 pp 74ndash91 2015

[47] F Wei and W Chan ldquoe cooperative stability evolutionarygame analysis of the military-civilian collaborative innovationfor Chinarsquos satellite industryrdquo Mathematical Problems inEngineering vol 2019 Article ID 3938716 17 pages 2019

[48] Z Zhang and J T Yu ldquoGame simulation analysis of radicalinnovation processes of high-tech enterprises based onWoO-EGTmodelrdquoTehnicki Vjesnik-Technical Gazette vol 26 no 2pp 518ndash526 2019

[49] Q T Zhu and C H Liu ldquoe application of MATLABsimulation technology on evolutionary game analysisrdquo Ap-plied Mechanics and Materials vol 687ndash691 pp 1619ndash16212014

[50] X H Wang R W Lu H Yu and D Li ldquoStability of theevolutionary game system and control strategies of behaviorinstability in coal mine safety managementrdquo Complexityvol 2019 Article ID 6987427 14 pages 2019

[51] R W Lu X H Wang and D Li ldquoA fractional supervisiongame model of multiple stakeholders and numerical simu-lationrdquo Mathematical Problems in Engineering vol 2017Article ID 9123624 9 pages 2017

[52] L Tong and Y Dou ldquoSimulation study of coal mine safetyinvestment based on system dynamicsrdquo International Journalof Mining Science and Technology vol 24 no 2 pp 201ndash2052014

16 Complexity

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International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


AnalysisInternational Journal of


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Submit your manuscripts atwwwhindawicom

sustainable development of coal mining industry and is oneof the problems that China need to solve urgently

In order to reduce the occurrence of coal-mine safetyaccidents improve the current situation of coal-mine safetyproduction and ensure the sustainable development of coalmining industry domestic and foreign scholars have studiedeffective countermeasures to promote coal-mine safetyproduction from different perspectives and aspects

e first research stream of coal-mine safety productionenhancement focuses on the human factors such as con-trolling the unsafe behavior of miners e unsafe behaviorof miners is the most direct cause of coal-mine safety ac-cidents and the main reason for destroying the normaloperation of coal-mine safety production [4ndash6] e minersalways face a trade-off between work stress for safe operationand psychological benefits for unsafe operation andreaching higher psychological and spiritual benefits mighthave strong substitution effects with safe operationerefore alleviating the work stress response of miners andimproving the safety behavior of them are the key to en-suring the normal operation of coal-mine safety productionAt present most scholars explore the generating mechanismof the unsafe behavior of miners and results indicate that theindividual characteristics (safety awareness knowledge andskills safety attitude physical quality and experience) ofminers [7ndash9] and environmental factors [10ndash12] (workingenvironment equipment environment social environmentfamily environment etc) have significant impact on theminersrsquo behavioral decisions which will in turn affect thesafety production of coal mining enterprises

e second research stream of coal-mine safety pro-duction enhancement focuses on the organizational factors[13ndash15] e organizationrsquos investments in safety culturepropaganda safety training safety regulations and safetyincentives will affect the level of the safety climate and thusaffect the minersrsquo behavioral decisions ultimately affectingthe safety production of coal mining enterprises In shortthe level of safety climate of organization plays an importantrole in the operation of coal-mine safety production and theimprovement level of safety climate depends on the orga-nizationrsquos emphasis and the attention degree on safety[16 17] According to the theory of social exchange [18ndash20]the safety climate level of organization and the behavioraldecision of miners are equivalent and reciprocal At the sametime the supervision of first-line managers also affects thebehavioral decision making of miners And the behavioraldecision-making model of miners [21] indicates that theexpected total value of minersrsquo unsafe behavior is deter-mined by the decision weight function and the psychologicalvalue function and the decision weight function is closelyrelated to the supervision effect of supervisors Before theminers make decisions the supervision effect of supervisorswill affect the minersrsquo expectations of the taskrsquos interests inthe decision making it influences the decision weightfunction and the psychological value function and theninfluences the behavior decision which ultimately affects thesafety production level of coal-mine enterprises And somestudies [22 23] comprehensively analyzed human factorsand organizational factors involved in mining accidents and

determined the relationships among these factors e re-sults showed that the human factors including skill-basederrors routine violations and planned inappropriate op-eration and environmental factors had a higher relativeimportance in the accidents Moreover the environmentalfactors and human factors had a higher influence on unsafeacts

e research streams of the previous two focus on theinfluencing mechanism of internal and external factors(individual characteristics machinery and equipmentworking environment and organization management) oncoal-mine safety production and the ldquopeople-machine-ring-tuberdquo causal system is gradually formed to our knowledgemost of them analyze coal-mine safety production and itsinfluencing factors from static and a single perspective andthey are short of research on the interaction of variousfactors from the perspective of overall system neglecting thesubjective initiative of individual behavior

In order to make up for the above defects the thirdresearch stream of coal-mine safety production enhance-ment focuses on the gaming behaviors of stakeholders eearly game research studies [24ndash27] on coal-mine safetyproduction mainly analyzed the relationship between thecoal-mine regulators and coal enterprise and concluded thatthe coal enterprisersquos inadequate safety investment was thereal cause of the frequent accidents and proposed that thepenalty for the coal enterprisersquos unlawful production shouldbe strengthened in the short term ese studies provide apromising foundation to explain the high incidence of coalaccidents in China and improve the situation of coal-minesafety production However the above research studiesmainly focus on statically analyzing the game between twostakeholders and neglect the dynamic process of game playIn order to explain the dynamic process of coal-mine safetyproduction more systematically and comprehensively Liuet al [28] explored the use of evolutionary game theory todescribe the long-term dynamic process of multiplayer gameplaying in coal-mine safety regulation under the condition ofbounded rationality Furthermore the multiplayer evolu-tionary game was simulated by adopting system dynamics toanalyze the implementation effect of different penaltystrategies on the game process and game equilibrium Topromote the safety education level of Chinarsquos coal miningenterprises the government coal mining enterprises andemployees are included in the evolutionary game model toexplore the game relation and evolutionary path of thedecision-making behavior among the three stakeholders inthe safety management system [29 30] However they focusmainly on analyzing the game between the external entitiessuch as the government the enterprises themselves and theemployees from a macro perspective are short of researchon revealing the dynamic interactions among the actorsdirectly involved in the coal-mine accidents and also onproposals for effective interactions that will lead to improvedsafety outcomes Although Yu et al [31] constructed anevolutionary game model of workersrsquo behavior in coalmining enterprises only the static game between the twoagents such as the managers and miners was consideredActually the stakeholders in coal-mine safety production

2 Complexity










Complexity 3







(1)




(2)



as follows



dx



(4)




(5)


G(x y z) dy



H(x y z) dz




(6)


F(x y z) dx


G(x y z) dy


H(x y z) dz


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)




4 Complexity


J

zF(x y z)

zx

zF(x y z)

zy

zF(x y z)

zz

zG(x y z)

zx

zG(x y z)

zy

zG(x y z)

zz

zH(x y z)

zx

zH(x y z)

zy

zH(x y z)

zz

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

B1 B2 B3

B4 B5 B6

B7 B8 B9

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where












(9)









miners t1 gt t5









miners t5 gt 0



manager c6 gt 0




managers s3 gt s4




of managers c7 gt 0



managers s4 gt 0

Complexity 5












Organization


Safety supervision

Manager








s3 s2 + s4 minus c7

6 Complexity











Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018

















Complexity 3







(1)




(2)



as follows



dx



(4)




(5)


G(x y z) dy



H(x y z) dz




(6)


F(x y z) dx


G(x y z) dy


H(x y z) dz


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)




4 Complexity


J

zF(x y z)

zx

zF(x y z)

zy

zF(x y z)

zz

zG(x y z)

zx

zG(x y z)

zy

zG(x y z)

zz

zH(x y z)

zx

zH(x y z)

zy

zH(x y z)

zz

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

B1 B2 B3

B4 B5 B6

B7 B8 B9

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where












(9)









miners t1 gt t5









miners t5 gt 0



manager c6 gt 0




managers s3 gt s4




of managers c7 gt 0



managers s4 gt 0

Complexity 5












Organization


Safety supervision

Manager








s3 s2 + s4 minus c7

6 Complexity











Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018














(1)




(2)



as follows



dx



(4)




(5)


G(x y z) dy



H(x y z) dz




(6)


F(x y z) dx


G(x y z) dy


H(x y z) dz


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(7)




4 Complexity


J

zF(x y z)

zx

zF(x y z)

zy

zF(x y z)

zz

zG(x y z)

zx

zG(x y z)

zy

zG(x y z)

zz

zH(x y z)

zx

zH(x y z)

zy

zH(x y z)

zz

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

B1 B2 B3

B4 B5 B6

B7 B8 B9

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where












(9)









miners t1 gt t5









miners t5 gt 0



manager c6 gt 0




managers s3 gt s4




of managers c7 gt 0



managers s4 gt 0

Complexity 5












Organization


Safety supervision

Manager








s3 s2 + s4 minus c7

6 Complexity











Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018









J

zF(x y z)

zx

zF(x y z)

zy

zF(x y z)

zz

zG(x y z)

zx

zG(x y z)

zy

zG(x y z)

zz

zH(x y z)

zx

zH(x y z)

zy

zH(x y z)

zz

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

B1 B2 B3

B4 B5 B6

B7 B8 B9

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where












(9)









miners t1 gt t5









miners t5 gt 0



manager c6 gt 0




managers s3 gt s4




of managers c7 gt 0



managers s4 gt 0

Complexity 5












Organization


Safety supervision

Manager








s3 s2 + s4 minus c7

6 Complexity











Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018



















Organization


Safety supervision

Manager








s3 s2 + s4 minus c7

6 Complexity











Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018


















Complexity 7





y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018












y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1Pr

(x)

86 100 2 4t

(a)

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

3 60 71 42 5t

(b)

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

05 15 25 3530 1 42t

(c)


8 Complexity




0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018











0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 2515 30 1 2t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


Complexity 9



0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018










0

01

02

03

04

05

06

07

08

09

1Pr

(x)

05 150 21t

y = 02 z = 02y = 03 z = 03y = 04 z = 04y = 05 z = 05

y = 06 z = 06y = 07 z = 07y = 08 z = 08y = 09 z = 09

(a)

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

30 1 42 5t

x = 02 z = 02x = 03 z = 03x = 04 z = 04x = 05 z = 05

x = 06 z = 06x = 07 z = 07x = 08 z = 08x = 09 z = 09

(b)

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

10 20 30 400t

x = 02 y = 02x = 03 y = 03x = 04 y = 04x = 05 y = 05

x = 06 y = 06x = 07 y = 07x = 08 y = 08x = 09 y = 09

(c)


10 Complexity


4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018









4 Discussion




y = 05 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (x

)

05 150 21t

(a)

x = 04 z = 06

0

01

02

03

04

05

06

07

08

09

1

Pr (y

)

05 2515 30 1 2t

(b)

x = 04 y = 05

0

01

02

03

04

05

06

07

08

09

1

Pr (z

)

86 100 2 4t

(c)


Complexity 11




xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018











xyz

0

03

05

07

1

Pr

30 1 42 5t


xyz

0

03

05

07

1

Pr

05 15 250 1 2t


xyz

05 15 25 3530 1 2t

0

03

05

07

1


xyz

0

03

05

07

1

Pr

05 150 21t


12 Complexity




5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018











5 Conclusions



Complexity 13






Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018













Data Availability






Acknowledgments


References






14 Complexity



































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018










































Complexity 15
















16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018























16 Complexity








Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








game modelling and strategy research on trilateral evolution for...

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