research on taxi driver strategy game evolution...

Research ArticleResearch on Taxi Driver Strategy Game Evolution withCarpooling Detour

Wei Zhang Ruichun He Changxi Ma and Mingxia Gao

School of Traffic and Transportation Lanzhou Jiaotong University Lanzhou 730070 China

Correspondence should be addressed to Ruichun He tranman163com

Received 9 October 2017 Accepted 31 December 2017 Published 28 January 2018

Academic Editor Giulio E Cantarella

Copyright copy 2018 Wei Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

For the problem of taxi carpooling detour this paper studies driver strategy choice with carpooling detour The model of taxidriver strategy evolution with carpooling detour is built based on prospect theory and evolution game theory Driver stablestrategies are analyzed under the conditions of complaint mechanism and absence of mechanism respectively The results showthat passengerrsquos complaint mechanism can effectively decrease the phenomenon of driver refusing passengers with carpoolingdetour When probability of passenger complaint reaches a certain level the stable strategy of driver is to take carpooling detourpassengers Meanwhile limiting detour distance and easing traffic congestion can decrease the possibility of refusing passengersThese conclusions have a certain guiding significance to formulating taxi policy

1 Introduction

Taxi carpooling mode has the characteristics of improvingthe transportation efficiency easing the traffic pressure andreducing environmental pollution [1 2] In recent years manycities in China have begun to implement taxi carpoolingpolicy to solve the serious traffic problems Taxi carpoolingoperation is in the initial stage and the carpool policyis imperfect It is very necessary to study taxi carpoolingproblem in the present situation

Many scholars have carried out researches on the problemof carpooling At present most researches on carpooling arefocused on the problem of carpooling matching and pathoptimization [3ndash6] Aissat and Oulamara [7] proposed amethod of optimizing starting point position of driver andpassenger based on the heuristic algorithm and the resultscan minimize the travel cost and detour distance Santi et al[8] proposed a method of carpooling strategy optimizationbased on network which can shorten the passenger traveltime and improve the utilization rate of vehicles Shinde andThombre [9] solved the problemof carpooling path optimiza-tion based on genetic algorithms He et al [10] obtained theoptimal path by mining GPS positioning data Nourinejadand Roorda [11] designed a centralized and decentralized

optimization algorithms based on binary integer program-ming and dynamic auction-based multiagent for the prob-lem of matching passengers and drivers Huang et al [12]proposed the genetic-based carpooling route and matchingalgorithm for the multiobjective optimization problem Xiaet al [13] built an optimizationmodel of carpoolingmatchingand designed heuristic algorithm to solve it Chiou and Chen[14] proposed a dynamic matching method for carpoolingwhich can be used in mobile devices via ad hoc Wi-Fi net-works Boukhater et al [15] presented aGAwith a customizedfitness function that searches for the solution with minimaltravel distance efficient ride matching timely arrival andmaximum fairness which can be used in carpooling systemXiao et al [16] studied passengers matching problem basedon clustering and pattern recognition methods The aboveresearches establish the model of carpooling matching opti-mization and then find the optimalmatchingmode by heuris-tic algorithm or data mining algorithms which solve theproblem of the carpooling matching and path optimizationand provide theory support for carpooling implementation

Detour problem is a common phenomenon of taxicarpooling In general detour passengers will get more costdiscount than usual carpooling to make up for the lossescaused by detour But from the perspective of the drivers

HindawiJournal of Advanced TransportationVolume 2018 Article ID 2385936 8 pageshttpsdoiorg10115520182385936

2 Journal of Advanced Transportation

O

D1

D2

Figure 1 Travel routes of carpooling passengers

driversrsquo income will be affected Driver may bemore resistantto carpooling detour which makes carpooling detour impos-sible in reality So it is necessary to study the problemof driverstrategy with carpooling detour The study has an importantsignificance to the implementation of carpooling systemHowever few researches involve the problem of carpoolingdetour Therefore this paper establishes a model of driverstrategy evolution based on prospect theory and evolutionarygame theory and studies the problem of driver strategy withcarpooling detour

2 Problem Description andResearch Framework

21 Problem Description Suppose two passengers departfrom the same location119874The destination of passenger 1 is1198631and that of passenger 2 is1198632 The best path for passenger 1 is1198741198631 and passenger 2 is 1198741198632 1198741198631 and 1198741198632 do not coincideas shown in Figure 1There are three road sections in Figure 1where 1198741198631 is section 1 1198741198632 is section 2 11986311198632 is section 3and |1198741198631| = 1198971 |1198741198632| = 1198971 |11986311198632| = 1198973 The traffic statusof each section is uncertain The traffic status of the section119894 is represented as 119895119894 When the traffic status of the section 119894is normal 119895119894 = 1 When the status is congestion 119895119894 = 2 Thetraffic congestion rate of the section 119894 is represented as 120593119894Thearrival time of the section 119894 with normal traffic is representedas 119905119894 The waiting time of the section 119894 with congestion isrepresented as 119903119894 Now the two passengers ride the sametaxi through path 11987411986311198632 That is passenger 1 is sent to hisdestination first and then passenger 2 Passenger 1 will pay apart of the fare and payment ratio is 120579 Passenger 2 will getmore discount than passenger 1 because he makes a detourThedriver faceswith two strategies taking the two passengersor refusing themThis paper will study the problemof driversrsquostability strategy under the above conditions

22 Research Framework The evolution game theory is aneffectivemethod to study human stability strategyThe theoryanalyzes problem on the premise of the bounded rational-ity It believes that the human behaviors reveal boundedrationality and human strategies reach stability graduallythrough constant adjustment [17 18] Evolutionary gametheory studies stable strategies of human behaviors whichsolves the problem of full rational analysis divorcing from

reality [19ndash21] The evolution game theory has become oneof the most important fields of modern game theory

The evolutionary game model has been applied intoanalysis of stable strategies with bounded rationality but thetheory model still shows the defect which has characteristicof full rationality In the payoff matrix of the evolutionarygame model revenue value is usually defined as directbenefits of each actor under different strategies That is thefundamental condition of evolutionary game is that actor canaccurately obtain revenue values of different strategies whichcoincides with traditional full rational game But the actorswhose cognitive ability computational ability and judgmentability cannot achieve such a high requirement are not fullrational So the actors are not able to obtain accurate revenuevaluesThen the fundamental condition of evolutionary gamecan not be satisfied and the subsequent evolutionary analysiswill lose significance

In this paper prospect theory is introduced into evolu-tionary game model to solve above problem Prospect theoryis a cross research theory of psychology and behavioralscience which reveals the human psychology of decision-making This theory describes peoplersquos decision psychologyrules in uncertain environments [22] and reflects more trulypeoplersquos behavior tendency According to prospect theorystrategy prospect value describes peoplersquos perception resultsof revenue for the strategy with respect to personal psycho-logical expectations [23 24] So strategy prospect value ismore close to peoplersquos judgment result reflecting boundedrationality [25ndash27] Therefore this paper combines prospecttheory and evolutionary game theory and establishes driverstrategy evolution model based on prospect value to studydriver stable strategy under the condition of carpoolingdetour with strategic prospect value instead of strategicrevenue value of game model The model includes two partsdriver strategy prospectmodel and evolutionary gamemodelFirstly driver strategy prospect model is established Theprospect value of each strategy is obtained through theestablished model Then evolutionary game model is builtbased on strategy prospect value using strategy prospectvalue as strategic revenue Driver stable strategy is analyzedby replicated dynamicmechanismThismethod improves thetraditional evolutionary game model and makes up for thefull rationality shortcoming of payoffmatrix in the traditionalevolutionary game model which makes research work closerto reality

This paper studies driver stable strategy based on theimproved model The study finds out that refusing behaviorsappear easily with carpooling detour So passenger complaintmechanism is introduced next Driver stable strategy isstudied with passenger complaint mechanism Eventually weconfirm that passenger complaint mechanism is an effectivemethod to avoid refusing behaviors We also find out relatedregulations

3 Modeling

31 Driver Strategy Prospect Value Suppose taxi chargingstandard stipulates that initiate fee is 119891119904yen119889 km 119891119903yen perkilometermore than 119889 kilometers andwaiting fee is119891119902yenmin

Journal of Advanced Transportation 3

Then when travel distance is 119897 and waiting time is 119903cost119885(119897 119903) is

119885 (119897 119903) =

119891119904 + 119903119891119902 if 119897 le 119889(119897 minus 119889) 119891119903 + 119891119904 + 119903119891119902 if 119897 gt 119889

(1)

If two passengers take the same taxi cost of passenger 1 is

1198621 =

120579119885 (1198971 0) if 1198951 = 1120579119885 (1198971 1199031) if 1198951 = 2

(2)

The travel route causes detour for passenger 2 So it isnecessary to reduce the cost of passenger 2 to make up forhis time loss Considering that the more the detour time thelower the detour cost the cost of passenger 2 is inverselyproportional to his nondetour time following relationalexpression given

1198622 =

120579119885 (1198972 0)1199052

1199051 + 1199053if 1198951 = 1 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199033if 1198951 = 1 1198953 = 2

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031if 1198951 = 2 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031 + 1199033if 1198951 = 2 1198953 = 2

(3)

If driver takes the two passengers in carpooling modestarting from119874 through1198631 before arriving in1198632 the driverrsquosincome is the sum of the two passengersrsquo costs

119868 = 1198621 + 1198622 (4)

If driver takes only a passenger starting from 119874 through1198631 before arriving in1198632 the driverrsquos income is

1198680 =

119885(1198971 + 1198973 0) if 1198951 = 1 1198953 = 1119885 (1198971 + 1198973 1199033) if 1198951 = 1 1198953 = 2119885 (1198971 + 1198973 1199031) if 1198951 = 2 1198953 = 1119885 (1198971 + 1198973 1199031 + 1199033) if 1198951 = 2 1198953 = 2

(5)

The driverrsquos income 1198680 when he takes only a passengerwhich is regarded as driver reference point then the driverrsquosgain relative to reference point is

119910119863 = 119868 minus 1198680 (6)

According to prospect theory value function is defined asfollows

119881(119910119863) =

(119910119863)120572 when 119910119863 ge 0minus120582 (minus119910119863)120573 when 119910119863 lt 0

(7)

where 120572 and 120573 (0 le 120572 120573 le 1) are risk attitude coefficientsThe bigger 120572 or 120573 is the more adventurous decision makertends to 120582 (120582 gt 1) is loss aversion coefficient which reflects

that decision maker is more sensitive to loss Value functionshows the decreasing sensitivity in the two directions ofgain and loss The result of the value function reflectsthe psychological revenue more realistically The parametersvalues 120572 = 089 120573 = 092 120582 = 225 aremore consistent withpsychological characteristic of decision maker [22]

Path 11987411986311198632 includes section 1 and section 3 Trafficcongestion rate of the path is defined as 12059313

12059313 =

(1 minus 1205931) (1 minus 1205933) if 1198951 = 1 1198953 = 1(1 minus 1205931) 1205933 if 1198951 = 1 1198953 = 21205931 (1 minus 1205933) if 1198951 = 2 1198953 = 112059311205933 if 1198951 = 2 1198953 = 2

(8)

The probability of traffic congestion which is perceivedby passenger is different from actual probability according toprospect theory The perceived probability of traffic conges-tion is

119882(12059313) =

(12059313)120594

((12059313)120594 + (1 minus 12059313)120594)1120594

if119910119863 ge 0

(12059313)120575

((12059313)120575 + (1 minus 12059313)120575)1120575

if119910119863 lt 0(9)

The parameter values most reflecting individual behaviorof decision maker are 120594 = 061 120575 = 069 [22] Thetransformation reflects that people tend to overestimate smallprobability events and underestimate medium and largeprobability events while people are relatively insensitive tothe intermediate stage Transformed probability is more closeto peoplersquos subjective probability

If the driver selects taking carpooling passenger strategythe prospect value 1198641198811198631 is

1198641198811198631 =2

sumV=1

2

sum119906=1

119882(12059313 (1198951 = 119906 1198953 = V)) 119881

sdot (119910119863 (1198951 = 119906 1198953 = V)) (10)

where 12059313(1198951 = 119906 1198953 = V) is traffic congestion probabilityunder the condition of 1198951 = 119906 and 1198953 = V 119910119863(1198951 = 119906 1198953 = V)is driver gain under the condition of 1198951 = 119906 and 1198953 = V

Because driver reference point is the gain when he takesonly a passenger the prospect value is 0 if the driver takes onlya passenger the prospect value is the result of 119868 = 0 conditionif the driver does not take any passenger

32 Evolutionary Analysis of Driver Carpooling StrategyDriver has two strategy choices taking carpooling detourpassengers (strategy 1) and refusing carpooling detour pas-sengers (strategy 2) If the driver selects strategy 1 and thepassengers select sharing the taxi carpooling succeeds thenthe driverrsquos prospect value is represented as1198641198811198631 If the driverselects strategy 2 and the passengers select riding the taxilonely the driver takes only a passenger then the prospect


value is 0 If the driverrsquos strategy and passengersrsquo strategy arenot different the driver does not take any passenger and theprospect value is represented as 1198641198811198632

Suppose the percentage of passengers choosing carpool-ing detour strategy is 1199011 and the percentage of driverschoosing carpooling detour strategy is 119902 Expected gains ofdriver choosing strategy 1 and strategy 2 respectively are asfollows

1199061 = 1198641198811198631 1199011 + 1198641198811198632 (1 minus 1199011)1199062 = 1198641198811198632 1199011

(11)

Average expected gain is

119906 = 1199061119902 + 1199062 (1 minus 119902)= 1198641198811198631 1199011119902 + 1198641198811198632 (1 + 1199011 (1 minus 2119902))

(12)

Replicator dynamic equation of driver percentage is

119865 (119902) = 119889119902119889119905 = 119902 (1199061 minus 119906)

= 119902 (1 minus 119902) ((1198641198811198631 minus 21198641198811198632 ) 1199011 + 1198641198811198632 ) (13)

Suppose 119865(119902) = 119889119902119889119905 = 0 then 119902 = 0 119902 = 1 119901lowast1 =1198641198811198632 (21198641198811198632 minus 1198641198811198631 )

According to the condition we know 1198641198811198632 lt 0 Thestability analysis is as follows

(1) When 1198641198811198631 minus 21198641198811198632 gt 0A if 1199011 = 119901lowast1 then 119865(119902) = 0 1198651015840(119902) = 0 here any strategy

may be stableB if 1199011 gt 119901lowast1 then 1198651015840(0) gt 0 1198651015840(1) lt 0 here 119902 = 1

is stable strategy That is when the percentage of passengerschoosing carpooling is more than 119901lowast1 driver will choosestrategy 1

C if 1199011 lt 119901lowast1 then 1198651015840(0) lt 0 1198651015840(1) gt 0 here119902 = 0 is stable strategy That is when the percentage ofpassengers choosing carpooling is low than 119901lowast1 driver willchoose strategy 2

(2)When1198641198811198771 minus21198641198811198772 lt 0 inevitably 1199011 gt 119901lowast1 here 119902 = 0is stable strategy and driver will choose strategy 2

Through the above analysis driver stable strategy istaking passengers only if 1198641198811198631 minus 21198641198811198632 gt 0 and 1199011 gt 119901lowast1 otherwise stable strategy is refusing passengers

4 Researches on Driver Strategy Evolutionwith Complaint Mechanism

Driver income will be affected when detour occurs in car-pooling Drivers are inclined to refusing passengers Nextpassenger complaint mechanism is introduced to furtheranalyze driver strategy change with complaint mechanism

41 Prospect Value of Driver Strategy with Complaint Mech-anism Under the condition of passenger complaint mech-anism driver will make a choice carefully after consideringthe consequences of refusing passengers Driver has two

D

P

Takingpassengers

Refusingpassengers

Complaint No complaintEVR

1

EVR21 EVR

22

Figure 2 Driver strategies and prospect values

choices taking passengers and refusing passengers Whenthe behavior of refusing passengers occurs passengers willchoose the complaint strategies or no complaint strategiesThe specific strategies are shown in Figure 2 If driver selectstaking carpooling detour passengers the prospect value isstill1198641198811198631 if driver selects refusing passengers and passengersselect complaint the prospect value is 11986411988111986321 if driver selectsrefusing passengers and passengers select no complaint theprospect value is 11986411988111986322

When the driver selects refusing strategy (assuming thatonly passenger 1 is taken at this time) and the passengersselect complaint strategy the prospects value of the driver is

11986411988111986321 =2

sum119906=1

119882(12059313 (1198951 = 119906))119881 (minus119892) (14)

where 119892 is punishment for refusing behavior after complaintWhen the driver selects refusing strategy and the passen-

gers select no complaint strategy the prospects value of thedriver is

11986411988111986322 = 0 (15)

42 Stability Strategy Analysis Suppose the percentage ofpassengers choosing complaint strategy is 1199012 and the per-centage of drivers choosing carpooling detour strategy is 119902Expected gains of driver choosing strategy 1 and strategy 2respectively are as follows

11990611 = 119864119881119863111990612 = 119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)

(16)


1199061 = 11990611119902 + 11990612 (1 minus 119902)= 1198641198811198631 119902 + (119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)) (1 minus 119902)

(17)



119865 (119902) = 119889119902119889119905 = 119902 (11990611 minus 1199061) = 119902 (1198641198811198631

minus (1198641198811198631 119902 + (119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)) (1 minus 119902)))

= 119902 (1 minus 119902) (1198641198811198631 minus 119864119881119863211199012 minus 11986411988111986322 (1 minus 1199012))

(18)

Suppose 1198651015840(119902) = 0 then 119902 = 0 119902 = 1 119901lowast2 = (11986411988111986322 minus1198641198811198631 )(11986411988111986322 minus 11986411988111986321) Due to 11986411988111986322 = 0 119901lowast2 = 1198641198811198631 11986411988111986321


(1) When 1198641198811198631 lt 0A if 1199012 = 119901lowast2 then 119865(119902) = 0 1198651015840(119902) = 0 here any strategy



C if 1199012 lt 119901lowast2 then 1198651015840(0) lt 0 1198651015840(1) gt 0 here 119902 = 0is stable strategy That is when the percentage of passengerschoosing carpooling is lower than 119901lowast2 driver will choosestrategy 2

(2) When 1198641198811198631 gt 0 inevitably 1198641198811198631 11986411988111986321 lt 0 1199011 gt 119901lowast1 here 119902 = 1 is stable strategy and driver will choose strategy 1

Through the above analysis drivers will select takingcarpooling passengers strategy unless 1198641198811198631 lt 0 and 1199012 gt 119901lowast2

5 Driver Evolution Strategies Comparisonunder the Different Mechanisms

(1)When 1198641198811198631 gt 0 Only tomeet the condition that the initialpercentage of passengers choosing carpooling detour strategyis more than 119901lowast1 is driversrsquo stable strategy taking carpoolingdetour passengers under the absence of complaint mecha-nism however driversrsquo stable strategy is taking carpoolingdetour passengers under the compliant mechanism

(2) When 1198641198811198631 lt 0

A If 1198641198811198631 minus 21198641198811198632 lt 0 Driversrsquo stable strategy is refusingcarpooling passengers under the absence of complaint mech-anism however driversrsquo stable strategy is taking carpoolingdetour passengers under the compliant mechanism as longas the condition that the initial percentage of passengerschoosing complaint strategy is more than 119901lowast2 is satisfied

B If 1198641198811198631 minus 21198641198811198632 gt 0 If the initial percentage of passengerschoosing carpooling detour strategy is more than 119901lowast1 driversrsquostable strategy is taking carpooling passengers under theabsence of complaint mechanism if the initial percentage ofchoosing complaint strategy is more than 119901lowast2 driversrsquo stablestrategy is taking carpooling passengers under the compliantmechanism

Under the above conditions prove 119901lowast1 gt 119901lowast2 as follows

Proof

119864119881119863221198641198811198632 minus 1198641198811198631

minus 119864119881119863111986411988111986321

= 1198641198811198632 11986411988111986321 minus (21198641198811198632 minus 1198641198811198631 ) 1198641198811198631(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= 1198641198811198632 (11986411988111986321 minus 21198641198811198631 ) + (1198641198811198631 )2

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= (1198641198811198631 minus 1198641198811198632 )2 + 1198641198811198632 (11986411988111986321 minus 1198641198811198632 )

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

(19)

Due to 1198641198811198631 minus 21198641198811198632 gt 0 11986411988111986321 lt 0 1198641198811198632 lt 0 and 11986411988111986321 lt1198641198811198632 we can know 1198641198811198632 (21198641198811198632 minus 1198641198811198631 ) minus 1198641198811198631 11986411988111986321 gt 0that is 119901lowast1 gt 119901lowast2

Through the above analysis the complaint mechanismmakes the conditions of driver stabilizing at taking car-pooling detour strategy easier to be satisfied The complaintmechanism can reduce the rejection rate of drivers

6 Example Analysis

Suppose taxi charging standard stipulates that initiate fee is10yen per 3 km 14yen per kilometer more than 3 kilometers andwaiting fee is 12yen per 25min Two passengers set out fromthe same location119874 to different destinationsThe destinationof passenger 1 is1198631 and that of passenger 2 is1198632They intendto ride the same taxi It is known that 1198971 = 1198972 = 5 and1198973 = 1 Travel speed is 30 km per hour Travel time is twice asnormal condition when traffic congestion occurs The trafficcongestion rate of each section is 120593 = 05 and carpoolingpayment ratio is 120579 = 07

We can know 119901lowast1 = 1198641198811198772 (21198641198811198772 minus 1198641198811198771 ) = 06 underthe absence of complaint mechanism 119902 = 1 is driversrsquo stablestrategywhen119901 gt 06That is driversrsquo stable strategy is takingpassengers if the initial percentage of passengers choosingcarpooling detour strategy is more than 60

Suppose driverrsquos punishment is 119892 = 50 under the com-plaint mechanismWe can know 119901lowast2 = (11986411988111987722 minus1198641198811198771 )(11986411988111987722 minus11986411988111987721) = 017 under the condition 119902 = 1 is driversrsquo stablestrategy when 119901 gt 017 That is driversrsquo stable strategyis taking passengers if the initial percentage of passengerschoosing complaint strategy is more than 17

So under the complaint mechanism the conditions thatcause driver to select carpooling strategy are more easilysatisfied and drivers tend to take carpooling passengers atthis time

Thresholds 119901lowast1 and 119901lowast2 are influenced by the factorssuch as detour distance penalty payment ratio and trafficcongestion rate The influence analysis is as follows

Figure 3 shows the influences of detour distance on thethreshold under the two different mechanisms Figure 3(a)is the influences analysis under the absence of complaintmechanism and Figure 3(b) is the influences analysis under


00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072

Detour distance (KM)

plowast 1

(a) Influence of detour distance on threshold under the absence ofcomplaint mechanism

00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2


(b) Influence of detour distance on threshold under the complaintmechanism

Figure 3 Influence of detour distance on threshold

00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062

Traffic congestion rate

plowast 1

(a) Influence of traffic congestion rate on threshold under the absence ofcomplaint mechanism

00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2

(b) Influence of traffic congestion rate on threshold under the complaintmechanism

Figure 4 Influence of traffic congestion rate on threshold

the complaint mechanism We can see that the thresholdincreases gradually with detour distance increases Under theabsence of complaint mechanism the initial percentage ofpassengers choosing carpooling strategy needs to reach 53when detour distance is 0 the initial percentage needs toreach 71 when detour distance is 5 KM However under thecomplaint mechanism the initial percentage of passengerschoosing complaint strategy needs to only reach 7 whendetour distance is 0 the initial percentage needs to reach 33when detour distance is 5 KM

Figure 4 shows the influences of traffic congestion rateon the threshold under the two different mechanisms Fig-ure 4(a) is the influences analysis under the absence ofcomplaint mechanism and Figure 4(b) is the influencesanalysis under the complaint mechanism We can see that

the threshold increases gradually with traffic congestion rateincreases Under the absence of complaint mechanism theinitial percentage of passengers choosing carpooling strategyneeds to reach 52when traffic is certainly normal the initialpercentage needs to reach 60when traffic congestion occursinevitably However under the complaint mechanism theinitial percentage of passengers choosing complaint strategyneeds to only reach 5 when traffic is certainly normal theinitial percentage needs to reach 28 when traffic congestionoccurs inevitably

Figure 5 shows the influences of passenger paymentratio on the threshold under the two different mechanismsFigure 5(a) is the influences analysis under the absence ofcomplaint mechanism and Figure 5(b) is the influencesanalysis under the complaint mechanismWe can see that the


00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10

Passenger payment ratio

plowast 1

(a) Influence of payment ratio on threshold under the absence ofcomplaint mechanism

00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2

(b) Influence of payment ratio on threshold under the complaintmechanism

Figure 5 Influence of payment ratio on threshold

0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2

Figure 6 Influence of penalty on threshold

threshold decreases gradually with passenger payment ratioincreases The threshold of the absence of complaint mecha-nism is lower obviously than that of complaint mechanism

The influences of penalty on the threshold are shownin Figure 6 The threshold decreases gradually with penaltyincreases and the rate of decline slows gradually The thresh-old is about 75 when the penalty is less than 20yen Thethreshold remains at about 5 when the penalty is over 200yenand the continuing increase of the penalty has little effect onthe threshold There is no sense to set excessive penalty andtoo low penalty can not affect driversrsquo strategy choice So it isnecessary to set the appropriate penalty under the complaintmechanism

In summary the thresholds that can ensure drivers toselect taking carpooling strategy are more easily satisfiedunder the complaints mechanism Complaint mechanismcan reduce the rate of drivers refusing passengers and makesdetour possible

7 Conclusions

This paper studies the problem of taxi driverrsquos strategychoice under the condition of carpooling detour The modelcombines prospect theory and evolutionary game theory andimproves traditional evolutionary game model by replacingthe gain with prospect value which makes the model morefit in with the actual psychology of human beings Throughthe researches and analysis the following conclusions areobtained

(1) The behavior of drivers refusing passengers underthe condition of carpooling detour can easily happenThe passenger complaints mechanism is an effectivemeasure to reduce the driver refusing behavior

(2) Whether or not drivers choose the strategy of tak-ing carpooling detour passengers depends on theinitial percentage of passengers choosing carpoolingstrategy or complaint strategy Under the absenceof complaint mechanism driversrsquo stable strategy istaking passengers if the percentage of passengerschoosing carpooling strategy is more than the thresh-old 119901lowast1 Under the complaint mechanism driversrsquostable strategy is taking passengers if the percentage ofpassengers choosing complaint strategy is more thanthe threshold 119901lowast2

(3) The thresholds relate to detour distance traffic con-gestion rate payment ratio and penalty The thresh-olds increase gradually with detour distance or trafficcongestion rate increases The thresholds decreasegradually with payment ratio or penalty increases Itis an effective way to avoid driver refusing behaviorto limit detour distance ease traffic congestion andselect the appropriate payment ratio and penalty

Therefore the impacts of the factors such as detourdistance and traffic congestion have to be considered inthe implementation process of taxi carpooling system It is


necessary to provide a simple and effective way of complaintsto encourage passengers complaining actively in order tocontrol refusing behavior

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research was funded by National Natural Science Foun-dation of China (61364026 51408288 and 71661021) andYouth Science Foundation of Lanzhou Jiaotong University(2015032) The authors express their thanks to all whoparticipated in this research for their cooperation

References

[1] D Zhang T He Y Liu S Lin and J A Stankovic ldquoAcarpooling recommendation system for taxicab servicesrdquo IEEETransactions on Emerging Topics in Computing vol 2 no 3 pp254ndash266 2014

[2] R Javid A Nejat and M Salari ldquoThe environmental impactsof carpooling in the United Statesrdquo in Proceedings of theTransportation Land and Air Quality Conference 2016

[3] J Jamal A E Rizzoli R Montemanni and D Huber ldquoTourplanning and ride matching for an urban social carpoolingservicerdquo in Proceedings of the 5th International Conference onTransportation and Traffic Engineering (ICTTE rsquo16) Switzer-land July 2016

[4] W Shen C V Lopes and JW Crandall ldquoAn onlinemechanismfor ridesharing in autonomous mobility-on-demand systemsrdquoin Proceedings of the 25th International Joint Conference onArtificial Intelligence pp 475ndash481 New York USA 2016

[5] S Galland L Knapen A-U-H Yasar et al ldquoMulti-agentsimulation of individual mobility behavior in carpoolingrdquoTransportation Research Part C Emerging Technologies vol 45pp 83ndash98 2014

[6] S-K Chou M-K Jiau and S-C Huang ldquoStochastic set-basedparticle swarm optimization based on local exploration forsolving the carpool service problemrdquo IEEE Transactions onCybernetics vol 46 no 8 pp 1771ndash1783 2016

[7] K Aissat and A Oulamara ldquoDynamic ridesharing with inter-mediate locationsrdquo in Proceedings of the 2014 IEEE Symposiumon Computational Intelligence in Vehicles and TransportationSystems (CIVTS rsquo14) pp 36ndash42 USA December 2014

[8] P Santi G Resta M Szell S Sobolevsky S H Strogatz andC Ratti ldquoQuantifying the benefits of vehicle pooling withshareability networksrdquo Proceedings of the National Acadamy ofSciences of the United States of America vol 111 no 37 pp13290ndash13294 2014

[9] T Shinde and B Thombre ldquoAn effective approach for solvingcarpool service problems using genetic algorithm approach incloud computingrdquo International Journal of Advance Research inComputer Science and Management Studies vol 3 no 12 pp29ndash33 2015

[10] W He K Hwang and D Li ldquoIntelligent carpool routing forurban ridesharing by mining GPS trajectoriesrdquo IEEE Transac-tions on Intelligent Transportation Systems vol 15 no 5 pp2286ndash2296 2014

[11] M Nourinejad and M J Roorda ldquoAgent based model fordynamic ridesharingrdquo Transportation Research Part C Emerg-ing Technologies vol 64 pp 117ndash132 2016

[12] S-C Huang M-K Jiau and C-H Lin ldquoA genetic-algorithm-based approach to solve carpool service problems in cloudcomputingrdquo IEEE Transactions on Intelligent TransportationSystems vol 16 no 1 pp 352ndash364 2015

[13] J Xia K M Curtin W Li and Y Zhao ldquoA new model for acarpool matching servicerdquo PLoS ONE vol 10 no 6 Article IDe0129257 2015

[14] S-Y Chiou and Y-C Chen ldquoA mobile dynamic and privacy-preserving matching system for car and taxi poolsrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 579031 10pages 2014

[15] C M Boukhater O Dakroub F Lahoud M Awad and HArtail ldquoAn intelligent and fair GA carpooling scheduler as asocial solution for greener transportationrdquo in Proceedings ofthe 2014 17th IEEE Mediterranean Electrotechnical Conference(MELECON rsquo14) pp 182ndash186 Lebanon April 2014

[16] Q Xiao R-C He W Zhang and C-X Ma ldquoAlgorithmresearch of taxi carpooling based on fuzzy clustering and fuzzyrecognitionrdquo Journal of Transportation Systems Engineering andInformation Technology vol 14 no 5 pp 119ndash125 2014

[17] G Mallard Bounded rationality and behavioral economicsRoutledge Press London UK 2015

[18] P van den Berg and F J Weissing ldquoEvolutionary GameTheory and Personalityrdquo in Evolutionary Perspectives on SocialPsychology Evolutionary Psychology pp 451ndash463 SpringerInternational Publishing Cham 2015

[19] M S Eid I H El-Adaway andK T Coatney ldquoEvolutionary sta-ble strategy for postdisaster insurance Game theory approachrdquoJournal of Management in Engineering vol 31 no 6 Article ID04015005 2015

[20] C Wu Y Pei and J Gao ldquoEvolution game model of travelmode choice inmetropolitanrdquoDiscrete Dynamics in Nature andSociety vol 2015 Article ID 638972 11 pages 2015

[21] C S Gokhale and A Traulsen ldquoEvolutionary multiplayergamesrdquoDynamic Games and Applications vol 4 no 4 pp 468ndash488 2014

[22] A Tversky and D Kahneman ldquoAdvances in prospect theorycumulative representation of uncertaintyrdquo Journal of Risk andUncertainty vol 5 no 4 pp 297ndash323 1992

[23] J Wang and T Sun ldquoFuzzy multiple criteria decision makingmethod based onprospect theoryrdquo inProceedings of the Proceed-ing of the International Conference on InformationManagementInnovation Management and Industrial Engineering (ICIII rsquo08)vol 1 pp 288ndash291 Taipei Taiwan December 2008

[24] P A de Castro A Barreto Teodoro L I de Castro and SParsons ldquoExpected utility or prospect theory which better fitsagent-based modeling of marketsrdquo Journal of ComputationalScience vol 17 no part 1 pp 97ndash102 2016

[25] W Zhang and R C He ldquoDynamic route choice based onprospect theoryrdquo in Proceedings of the vol 138 pp 159ndash167

[26] M Abdellaoui H Bleichrodt O LrsquoHaridon and D van DolderldquoMeasuring loss aversion under ambiguity a method to makeprospect theory completely observablerdquo Journal of Risk andUncertainty vol 52 no 1 pp 1ndash20 2016

[27] L A Prashanth J Cheng F Michael M Steve and S CsabaldquoCumulative prospect theory meets reinforcement learningprediction and controlrdquo in Proceedings of the 33th InternationalConference on Machine Learning pp 2112ndash2121 New York NYUSA 2016

International Journal of

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Submit your manuscripts atwwwhindawicom


O

D1

D2

Figure 1 Travel routes of carpooling passengers

driversrsquo income will be affected Driver may bemore resistantto carpooling detour which makes carpooling detour impos-sible in reality So it is necessary to study the problemof driverstrategy with carpooling detour The study has an importantsignificance to the implementation of carpooling systemHowever few researches involve the problem of carpoolingdetour Therefore this paper establishes a model of driverstrategy evolution based on prospect theory and evolutionarygame theory and studies the problem of driver strategy withcarpooling detour

2 Problem Description andResearch Framework

21 Problem Description Suppose two passengers departfrom the same location119874The destination of passenger 1 is1198631and that of passenger 2 is1198632 The best path for passenger 1 is1198741198631 and passenger 2 is 1198741198632 1198741198631 and 1198741198632 do not coincideas shown in Figure 1There are three road sections in Figure 1where 1198741198631 is section 1 1198741198632 is section 2 11986311198632 is section 3and |1198741198631| = 1198971 |1198741198632| = 1198971 |11986311198632| = 1198973 The traffic statusof each section is uncertain The traffic status of the section119894 is represented as 119895119894 When the traffic status of the section 119894is normal 119895119894 = 1 When the status is congestion 119895119894 = 2 Thetraffic congestion rate of the section 119894 is represented as 120593119894Thearrival time of the section 119894 with normal traffic is representedas 119905119894 The waiting time of the section 119894 with congestion isrepresented as 119903119894 Now the two passengers ride the sametaxi through path 11987411986311198632 That is passenger 1 is sent to hisdestination first and then passenger 2 Passenger 1 will pay apart of the fare and payment ratio is 120579 Passenger 2 will getmore discount than passenger 1 because he makes a detourThedriver faceswith two strategies taking the two passengersor refusing themThis paper will study the problemof driversrsquostability strategy under the above conditions

22 Research Framework The evolution game theory is aneffectivemethod to study human stability strategyThe theoryanalyzes problem on the premise of the bounded rational-ity It believes that the human behaviors reveal boundedrationality and human strategies reach stability graduallythrough constant adjustment [17 18] Evolutionary gametheory studies stable strategies of human behaviors whichsolves the problem of full rational analysis divorcing from

reality [19ndash21] The evolution game theory has become oneof the most important fields of modern game theory

The evolutionary game model has been applied intoanalysis of stable strategies with bounded rationality but thetheory model still shows the defect which has characteristicof full rationality In the payoff matrix of the evolutionarygame model revenue value is usually defined as directbenefits of each actor under different strategies That is thefundamental condition of evolutionary game is that actor canaccurately obtain revenue values of different strategies whichcoincides with traditional full rational game But the actorswhose cognitive ability computational ability and judgmentability cannot achieve such a high requirement are not fullrational So the actors are not able to obtain accurate revenuevaluesThen the fundamental condition of evolutionary gamecan not be satisfied and the subsequent evolutionary analysiswill lose significance

In this paper prospect theory is introduced into evolu-tionary game model to solve above problem Prospect theoryis a cross research theory of psychology and behavioralscience which reveals the human psychology of decision-making This theory describes peoplersquos decision psychologyrules in uncertain environments [22] and reflects more trulypeoplersquos behavior tendency According to prospect theorystrategy prospect value describes peoplersquos perception resultsof revenue for the strategy with respect to personal psycho-logical expectations [23 24] So strategy prospect value ismore close to peoplersquos judgment result reflecting boundedrationality [25ndash27] Therefore this paper combines prospecttheory and evolutionary game theory and establishes driverstrategy evolution model based on prospect value to studydriver stable strategy under the condition of carpoolingdetour with strategic prospect value instead of strategicrevenue value of game model The model includes two partsdriver strategy prospectmodel and evolutionary gamemodelFirstly driver strategy prospect model is established Theprospect value of each strategy is obtained through theestablished model Then evolutionary game model is builtbased on strategy prospect value using strategy prospectvalue as strategic revenue Driver stable strategy is analyzedby replicated dynamicmechanismThismethod improves thetraditional evolutionary game model and makes up for thefull rationality shortcoming of payoffmatrix in the traditionalevolutionary game model which makes research work closerto reality

This paper studies driver stable strategy based on theimproved model The study finds out that refusing behaviorsappear easily with carpooling detour So passenger complaintmechanism is introduced next Driver stable strategy isstudied with passenger complaint mechanism Eventually weconfirm that passenger complaint mechanism is an effectivemethod to avoid refusing behaviors We also find out relatedregulations

3 Modeling

31 Driver Strategy Prospect Value Suppose taxi chargingstandard stipulates that initiate fee is 119891119904yen119889 km 119891119903yen perkilometermore than 119889 kilometers andwaiting fee is119891119902yenmin



119885 (119897 119903) =

119891119904 + 119903119891119902 if 119897 le 119889(119897 minus 119889) 119891119903 + 119891119904 + 119903119891119902 if 119897 gt 119889

(1)


1198621 =

120579119885 (1198971 0) if 1198951 = 1120579119885 (1198971 1199031) if 1198951 = 2

(2)


1198622 =

120579119885 (1198972 0)1199052

1199051 + 1199053if 1198951 = 1 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199033if 1198951 = 1 1198953 = 2

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031if 1198951 = 2 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031 + 1199033if 1198951 = 2 1198953 = 2

(3)


119868 = 1198621 + 1198622 (4)


1198680 =

119885(1198971 + 1198973 0) if 1198951 = 1 1198953 = 1119885 (1198971 + 1198973 1199033) if 1198951 = 1 1198953 = 2119885 (1198971 + 1198973 1199031) if 1198951 = 2 1198953 = 1119885 (1198971 + 1198973 1199031 + 1199033) if 1198951 = 2 1198953 = 2

(5)


119910119863 = 119868 minus 1198680 (6)


119881(119910119863) =


(7)




12059313 =


(8)


119882(12059313) =

(12059313)120594

((12059313)120594 + (1 minus 12059313)120594)1120594

if119910119863 ge 0

(12059313)120575

((12059313)120575 + (1 minus 12059313)120575)1120575

if119910119863 lt 0(9)



1198641198811198631 =2

sumV=1

2

sum119906=1

119882(12059313 (1198951 = 119906 1198953 = V)) 119881

sdot (119910119863 (1198951 = 119906 1198953 = V)) (10)







1199061 = 1198641198811198631 1199011 + 1198641198811198632 (1 minus 1199011)1199062 = 1198641198811198632 1199011

(11)


119906 = 1199061119902 + 1199062 (1 minus 119902)= 1198641198811198631 1199011119902 + 1198641198811198632 (1 + 1199011 (1 minus 2119902))

(12)


119865 (119902) = 119889119902119889119905 = 119902 (1199061 minus 119906)

= 119902 (1 minus 119902) ((1198641198811198631 minus 21198641198811198632 ) 1199011 + 1198641198811198632 ) (13)












D

P

Takingpassengers

Refusingpassengers


1

EVR21 EVR

22




11986411988111986321 =2

sum119906=1

119882(12059313 (1198951 = 119906))119881 (minus119892) (14)



11986411988111986322 = 0 (15)


11990611 = 119864119881119863111990612 = 119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)

(16)



(17)



119865 (119902) = 119889119902119889119905 = 119902 (11990611 minus 1199061) = 119902 (1198641198811198631



(18)











(2) When 1198641198811198631 lt 0




Proof

119864119881119863221198641198811198632 minus 1198641198811198631

minus 119864119881119863111986411988111986321


= 1198641198811198632 (11986411988111986321 minus 21198641198811198631 ) + (1198641198811198631 )2

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= (1198641198811198631 minus 1198641198811198632 )2 + 1198641198811198632 (11986411988111986321 minus 1198641198811198632 )

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

(19)



6 Example Analysis








00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072


plowast 1


00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2




00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062


plowast 1


00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2








00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119885 (119897 119903) =

119891119904 + 119903119891119902 if 119897 le 119889(119897 minus 119889) 119891119903 + 119891119904 + 119903119891119902 if 119897 gt 119889

(1)


1198621 =

120579119885 (1198971 0) if 1198951 = 1120579119885 (1198971 1199031) if 1198951 = 2

(2)


1198622 =

120579119885 (1198972 0)1199052

1199051 + 1199053if 1198951 = 1 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199033if 1198951 = 1 1198953 = 2

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031if 1198951 = 2 1198953 = 1

120579119885 (1198972 0)1199052

1199051 + 1199053 + 1199031 + 1199033if 1198951 = 2 1198953 = 2

(3)


119868 = 1198621 + 1198622 (4)


1198680 =

119885(1198971 + 1198973 0) if 1198951 = 1 1198953 = 1119885 (1198971 + 1198973 1199033) if 1198951 = 1 1198953 = 2119885 (1198971 + 1198973 1199031) if 1198951 = 2 1198953 = 1119885 (1198971 + 1198973 1199031 + 1199033) if 1198951 = 2 1198953 = 2

(5)


119910119863 = 119868 minus 1198680 (6)


119881(119910119863) =


(7)




12059313 =


(8)


119882(12059313) =

(12059313)120594

((12059313)120594 + (1 minus 12059313)120594)1120594

if119910119863 ge 0

(12059313)120575

((12059313)120575 + (1 minus 12059313)120575)1120575

if119910119863 lt 0(9)



1198641198811198631 =2

sumV=1

2

sum119906=1

119882(12059313 (1198951 = 119906 1198953 = V)) 119881

sdot (119910119863 (1198951 = 119906 1198953 = V)) (10)







1199061 = 1198641198811198631 1199011 + 1198641198811198632 (1 minus 1199011)1199062 = 1198641198811198632 1199011

(11)


119906 = 1199061119902 + 1199062 (1 minus 119902)= 1198641198811198631 1199011119902 + 1198641198811198632 (1 + 1199011 (1 minus 2119902))

(12)


119865 (119902) = 119889119902119889119905 = 119902 (1199061 minus 119906)

= 119902 (1 minus 119902) ((1198641198811198631 minus 21198641198811198632 ) 1199011 + 1198641198811198632 ) (13)












D

P

Takingpassengers

Refusingpassengers


1

EVR21 EVR

22




11986411988111986321 =2

sum119906=1

119882(12059313 (1198951 = 119906))119881 (minus119892) (14)



11986411988111986322 = 0 (15)


11990611 = 119864119881119863111990612 = 119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)

(16)



(17)



119865 (119902) = 119889119902119889119905 = 119902 (11990611 minus 1199061) = 119902 (1198641198811198631



(18)











(2) When 1198641198811198631 lt 0




Proof

119864119881119863221198641198811198632 minus 1198641198811198631

minus 119864119881119863111986411988111986321


= 1198641198811198632 (11986411988111986321 minus 21198641198811198631 ) + (1198641198811198631 )2

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= (1198641198811198631 minus 1198641198811198632 )2 + 1198641198811198632 (11986411988111986321 minus 1198641198811198632 )

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

(19)



6 Example Analysis








00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072


plowast 1


00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2




00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062


plowast 1


00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2








00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1199061 = 1198641198811198631 1199011 + 1198641198811198632 (1 minus 1199011)1199062 = 1198641198811198632 1199011

(11)


119906 = 1199061119902 + 1199062 (1 minus 119902)= 1198641198811198631 1199011119902 + 1198641198811198632 (1 + 1199011 (1 minus 2119902))

(12)


119865 (119902) = 119889119902119889119905 = 119902 (1199061 minus 119906)

= 119902 (1 minus 119902) ((1198641198811198631 minus 21198641198811198632 ) 1199011 + 1198641198811198632 ) (13)












D

P

Takingpassengers

Refusingpassengers


1

EVR21 EVR

22




11986411988111986321 =2

sum119906=1

119882(12059313 (1198951 = 119906))119881 (minus119892) (14)



11986411988111986322 = 0 (15)


11990611 = 119864119881119863111990612 = 119864119881119863211199012 + 11986411988111986322 (1 minus 1199012)

(16)



(17)



119865 (119902) = 119889119902119889119905 = 119902 (11990611 minus 1199061) = 119902 (1198641198811198631



(18)











(2) When 1198641198811198631 lt 0




Proof

119864119881119863221198641198811198632 minus 1198641198811198631

minus 119864119881119863111986411988111986321


= 1198641198811198632 (11986411988111986321 minus 21198641198811198631 ) + (1198641198811198631 )2

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= (1198641198811198631 minus 1198641198811198632 )2 + 1198641198811198632 (11986411988111986321 minus 1198641198811198632 )

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

(19)



6 Example Analysis








00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072


plowast 1


00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2




00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062


plowast 1


00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2








00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119865 (119902) = 119889119902119889119905 = 119902 (11990611 minus 1199061) = 119902 (1198641198811198631



(18)











(2) When 1198641198811198631 lt 0




Proof

119864119881119863221198641198811198632 minus 1198641198811198631

minus 119864119881119863111986411988111986321


= 1198641198811198632 (11986411988111986321 minus 21198641198811198631 ) + (1198641198811198631 )2

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

= (1198641198811198631 minus 1198641198811198632 )2 + 1198641198811198632 (11986411988111986321 minus 1198641198811198632 )

(21198641198811198632 minus 1198641198811198631 ) 11986411988111986321

(19)



6 Example Analysis








00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072


plowast 1


00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2




00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062


plowast 1


00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2








00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



00 05 10 15 20 25 30 35 40 45 50

052054056058060062064066068070072


plowast 1


00 05 10 15 20 25 30 35 40 45 50

005

010

015

020

025

030

035

plowast 2




00 01 02 03 04 05 06 07 08 09 10

052

054

056

058

060

062


plowast 1


00 01 02 03 04 05 06 07 08 09 10

005

010

015

020

025

030


plowast 2








00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



00 01 02 03 04 05 06 07 08 09 1004

05

06

07

08

09

10


plowast 1


00 01 02 03 04 05 06 07 08 09 1000

01

02

03

04

05


plowast 2



0 50 100 150 200 250 300 350 400 450 500

00

01

02

03

04

05

06

07

08

Penalty (yen)

plowast 2





7 Conclusions










Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


research on taxi driver strategy game evolution...

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