Research ArticleA Novel Pricing Mechanism for User Coalition in Blockchain

Yi Jiang ,1 Xu Liu ,1,2 and Jun Dai1

1School of Information Engineering, Yangzhou University, Yangzhou Jiangsu 225127, China2School of Business, Victoria University, Melbourne VIC 3011, Australia

Correspondence should be addressed to Xu Liu; 1438239097@qq.com

Received 21 September 2020; Revised 15 October 2020; Accepted 23 October 2020; Published 28 November 2020

Academic Editor: Junwu Zhu

Copyright © 2020 Yi Jiang et al. This 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.

As the blockchain platform is widely used as a new trading way, both participants and transaction volume in the blockchain projectshave been growing by leaps and bounds. The generic mechanisms of ranking transaction priorities are heavily dependent on thetransaction fees the users append into each transaction; then, all transactions are ranked in the nonincreasing order according tothe transaction fee amounts, and the selected transactions will be packed into a new created block in order based on the rankingresults. However, more complex influence factors more than transaction fees on transaction priority ranking results are nottaken into consideration in the generic transaction priority ranking mechanisms, and a single user is the objective to createtransactions in these mechanisms. In order to optimize the generic transaction priority ranking mechanisms and enrichtransaction creation modes, a novel user-coalition-based transaction pricing mechanism (UCTPM) is proposed, and the usercoalition quality score, user coalition contribution degree, and the transaction type demand degree are formulated andintroduced into the UCTPM mechanism. Our research findings indicate that the UCTPM mechanism satisfies the economicattributes of budget balanced, individual rationality, and incentive compatibility when the user coalition contribution degreeincreases through theoretical proof and experimental analysis. Moreover, the UCTPM mechanism allows all the transactions tobe processed more efficiently by experimental analysis.

1. Introduction

In contrast to the traditional financial systems that heavilyrely on centralized supervision, digital cryptocurrencies useblockchain as the technical solutions providing a decentra-lized distributed ledger economic model for the currentfinancial market and enabling participants to freely join thiskind of open-market platform without constraints. Due tovarious excellent characteristics of blockchain technologiessuch as data immutability, information traceability, and nodepseudonyms, more participants have enjoyed such newtransaction methods provided by blockchain platforms. [1, 2]

With the emergence and constant improvement of vari-ous blockchain projects such as Bitcoin and Ethereum, thedigital cryptocurrencies issued by different blockchain pro-jects have attracted a large number of participants to contrib-ute to the computational power in mining activities which isto compete for being the first valid participant solving theproof-of-work-based cryptographic puzzle then to receive acertain amount of lucrative cryptocurrency as a mining

reward. In detail, among the blockchain projects where theconsensus process is based on proof of work (PoW), newblocks are normally generated by the participants calledminers who continuously perform massive hash calculationsto obtain the full solution for the hash puzzles, and the minerwho firstly gains the full solution is granted the right to addthese selected transactions into a new created block; then,he or she can get the transaction fees as extra mining profitin addition to the fixed block reward once the new block iscommitted as valid to the main chain [3, 4].

During the transaction confirming process, all the partic-ipants can create transactions; when a node firstly generatesone transaction and broadcasts it to other nodes within thewhole blockchain network, a certain amount of transactionfee is needed to append along with the generated transaction(even though the transaction fee is not enforced to appendalong with the transaction); once the transaction is verifiedto be valid, then it will be added into the mempool waitingin queue to get processed by the miner who wins the miningcompetition; then, some transactions are selected to append

HindawiWireless Communications and Mobile ComputingVolume 2020, Article ID 8885179, 12 pageshttps://doi.org/10.1155/2020/8885179

into the new created block based on certain rules (generallyfrom the highest transaction fee down to the lowest fee).Once the full solution of the cryptographic puzzles is found,the newly mined block is added to the main chain and prop-agated through the network. The transaction fee, as an eco-nomic incentive method of blockchain, is one of theimportant and effective approaches to guarantee nodes ofparticipation in mining activities and transaction verificationduring the whole transaction confirming processes. Amongthe generic methods of transaction selection, miners nor-mally prefer these transactions with higher fees to appendinto a new block in order to optimize the total profit whilemining; as a result, users are stimulated to increase the trans-action fees to some extent with the purpose of getting trans-actions to be confirmed as soon as possible [5]. Moreover,users can perform strategic bidding by observing and analys-ing the dynamic status of transaction queuing states in themempool to estimate the transaction threshold fee (that is,the lowest transaction fee among all the transactions is beingadded into the new block), thus fluctuating the overall profitof miners and affecting the efficiency of blockchain networktransaction confirming processing as consequences [6].

As it has been considered about the continuous improve-ment and widespread use of smart contracts in blockchain,the transaction types have been expanded. In the currentPoW-based blockchain projects, the common transactiontypes can be divided into two main categories as token trans-fer class and smart contract operation class. In detail, thetoken transfer class covers transactions with differentamounts of token and lock-time settings (that is, the expectedtime for the transaction to be added into a new block), whilethe smart contract operation class includes calling, updating,and creating. Beyond these transaction types above, partici-pants also can convert the main chain tokens into the sidechain tokens in order to bring more functions for the wholenetwork under the applied advanced smart contracts; there-fore, the shifting evolution of smart contracts results in awider variety of transaction types [7, 8]. With all the nodesinvolved in the blockchain network are the behaviour sub-jects who are involved in transaction verification, transactioncreation, mining reward competition, and other activities viathe blockchain platform, and all the historical activity infor-mation is recorded in the relevant code fragment in theblockchain; this makes it possible to use such activity infor-mation as a basis to measure the quality and contributionof each node in the network.

In addition, for most mechanisms used in the transactionconfirming process in the blockchain, incentive compatibilityis of great importance for any participants to behave truth-fully when bidding the transaction fees, and the rare resourcein the transaction confirming process is the number of trans-actions which can be packed successfully during each roundof mining. In this paper, we strive to study the factors affect-ing the transaction confirming process, and we declare thatthe participants who are involved in the blockchain networkare user, user coalition, and miners for simplification.

As the fast development and application of blockchaintechnologies and the widespread usage of the digital eco-nomic system with such a technical foundation, a mechanism

where participants are encouraged to join more activities andbehave honestly is necessary for the blockchain market [9].Based on the analysis above, we proposed a user-coalition-based transaction pricing mechanism (UCTPM); this mech-anism consists of two algorithms: user coalition weightedtransaction priority (UCWTP) algorithm and transactionpriority rank-based pricing (TPRP) algorithm, and each ofthe algorithms corresponds to transaction priority determi-nation and pricing for the winning user coalitions, respec-tively. Although there are several researches that bring thetransaction size, historical transaction volume, and user wait-ing costs to calculate the transaction priority results, the cal-culation modes of these factors are not given in the generalsecond price auction model. [10] It needs to be emphasizedthat, in the UCWTP mechanism, the user coalition qualityscore, coalition contribution degree, and transaction typedemand degree are formulated in detail and introduced tooptimize the transaction priority algorithms that only focuson the single transaction fee. In addition, we consider thatthe participants join the user coalitions as the transaction cre-ation mode, which is fairly a novel transaction creationmode, and we believe that the main advantage to considersuch a new transaction creation mode is that the efficiencyof the transaction confirming process can be improved dueto the transactions that are selected by batch instead of byindividual, also it is verified via the experiments conductedin this paper.

Whereafter, it is also proved through theoretical proofthat the UCTPM mechanism proposed in this paper satisfiesthe economic attributes of budget balanced, individual ratio-nality, and incentive compatibility under the circumstancethat the user coalition contribution degree increases. Besides,it shows that the UCWTP algorithm in the proposedUCTPMmechanism can help to reduce the impact of a singletransaction fee on transaction priority ranking by an averageof 5.17% when compared to the traditional transaction prior-ity algorithm through experimental analysis.

Our contribution can be summarized as the followingthree:

(1) Design a new UCTPM mechanism to optimize thetraditional transaction priority algorithms by intro-ducing the user coalition quality score, coalitioncontribution degree, and transaction type demanddegree

(2) Adopt user coalition transaction creation modelinstead of an individual transaction creation modelto enrich the transaction creation modes for theblockchain

(3) Prove that nodes under the UCTPM mechanismcan be effectively stimulated to participants in theactivities such as transaction creation, transactionverification, and computing power competition forbookkeeping right, so as to improve the contribu-tion degree and quality score

The rest of the paper is structured as follows: Section 2gives a brief review of related work. Section 3 defines the basic

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concepts that are used in the UCTPM mechanism model.Section 4 describes the problem details. Section 5 formallyestablishes the models of the UCWTP algorithm and theTPRP algorithm that both consisted of the UCTPM mecha-nism. Section 6 presents the detailed algorithms of UCWTPand TPRP and theoretically verifies that the UCTPM mech-anism satisfies the economic attributes of individual rational-ity, budget balanced, and incentive compatibility as the usercoalition contribution degree increases. In Section 7, the pro-posed UCWTP algorithm can effectively help to reduce theimpact of the single transaction fee on transaction prioritythrough the experimental analysis, thus motivating user coa-lition to actively join the activities in the blockchain platform,and the transaction confirming process time is also reducedunder the user coalition transaction creation mode. Finally,this paper is summarized and some future work is discussedin Section 8.

2. Related Work

During the initial stage of the Bitcoin project, users need toprovide the default transaction fee, and miners are requiredto process the transactions according to the system settingseven for the zero fee transactions, whereas users prefer tooffer a higher transaction fee to attract miners in order toreduce the transaction processing waiting time with thegrowth of transaction volume and users [11]. As recordedin the official document of Bitcoin, the transaction fees arenot required for some certain types of transactions thoughthe zero transaction fees cannot be financially sustainablewith the development of Bitcoin [12].

As the emergence of transaction fees has led to the trans-formation of blockchain from a simple structure of mining toa market-based ecological structure, some researches andmethodologies have been studied about the influence factorson transaction fees. The game model is established in Kasa-hara and Kawahara’s research to analyse the impact of factorson transaction fees including the transaction flow-in rate,flow-out rate, and user waiting time [13]. Moreover, severalmechanisms such as providing a fixed transaction fee to usersand miners and the Vickrey-Clarke-Groves (VCG) auction-based pricing model are compared to analyse the equilibriumtransaction fee, due to the fee that essentially depends on thecost of involving in the infrastructure for miners to competein mining [14]. However, the fixed transaction fee is infeasi-ble in the long run according to the static partial equilibriummodel that is designed for the economic analysis of the trans-action fee [15].

In addition, the Bitcoin market attribute of incentivecompatibility is deeply studied, and the monopoly pricingmodel and random sampling pricing model are establishedwith the purpose of avoiding user utility improvement bylying the transaction fees, and the results of theoretical verifi-cation show that the monopoly pricing mechanism is nearincentive compatibility under the condition of enough usersand transaction volume [16].

The researches on transaction fees introduced above aremore focused on the user perspective, but the transaction feesare crucial to miners as well. Transaction fees as the extra

reward are the economical incentive to sustain mining oper-ations [17]. Furthermore, when miners cannot profit fromthe mining process, they may switch from the current block-chain platform to another one for mining [18]. Since the pastfew years that Bitcoin was invented, the fixed block rewardplays a much more important role in the whole mining reve-nue system; the average revenue is approximately 14 BTC perblock with the fixed block generation reward 12.5 BTC in2017; however, the situation starts to change somehow withthe decreasing fixed block reward per 4 years, and the highestoverall revenue is about 19.79 BTC per block; all the changesindicate that the transaction fees start to play a key role in theblockchain market and can affect the miner’s revenue to acertain extent [19, 20].

Nevertheless, transaction fees not only are an importantpart of the blockchain market economy that determines therevenue of both users and miners but also have great influ-ence on transaction priority ranking results which are thekey basis for the transaction confirming process. Under dif-ferent priority rules, the user transaction fee decisions arevarious [21]. Moreover, users prefer to increase the transac-tion fees for the higher transaction priority in the transactionconfirming process where only transaction fees directly affectpriority rank results; meanwhile, users with lower transactionfees are discouraged to create transactions due to prolongedwaiting time, thus leading to negative influence on the block-chain development [22, 23].

3. Concept Definition

Definition 1 (user coalition). Any node who creates transac-tions via the blockchain platform is called a user, and sucha node can be a miner as well. User coalition is a group withn ðn > 1Þ users to create transactions, and in writing, the usercoalition is set as CLk, k ∈ CLk = 1, 2,⋯, k. In particular, anyusers in the user coalition create their own transactions sev-erally and form a transaction set as the coalition’s transactionset.

Definition 2 (miner). The nodes who contribute to the com-putational power in the mining process are called miners.And there is only one miner m who will obtain the transac-tion fees and block rewards during each round of miningcompetition; moreover, the transactions of winning user coa-lition are processed by m.

Definition 3 (user coalition utility). Denote that the utility ofuser coalition kð∀k ∈ CLkÞ is uCLk = ðVk − pkÞ; that is, the util-ity is the difference value between the overall valuation of thetransactions and actual payment of any k.

Definition 4 (individual rationality). If there is no loss ofprofit for any k who participates in the mechanism, that is,uCLk ≥ 0 ð∀k ∈ CLkÞ, this demonstrates that the mechanismsatisfies the attribute of individual rationality.

Definition 5 (budget balanced). If all the income of the mech-anism comes from the total payment of winning user

3Wireless Communications and Mobile Computing

coalition without any external personnel, and the expendi-tures of the mechanism are all used to pay the miner whoprocesses the transaction without any value transfer, that is,∑k∈Wpk = paym, this illustrates that the mechanism satisfiesthe attribute of budget balanced, and the attribute of budgetbalanced ensures that there is no value to be transferred inor out from the mechanism.

Definition 6 (incentive compatibility). Denote the truthfulbid as bk, the lying bid as bk′ for kð∀k ∈ CLkÞ when k ð∀k ∈CLkÞ bids for the transaction set, and the corresponding util-ities are uCLk and uCLk′ , respectively. The mechanism is incen-tive compatible if one of the following two conditions is true:(1) it satisfies ∀k ∈ CLk, bk > bk′⟶ uCLk ≥ uCLk′ when k lowersthe transaction fee bid, or (2) there exists a strategy αk for k toincrease the transaction fee bid and strategy α∗k for k toincrease the quality score, when it satisfies ∀k ∈ CLk, uðα∗k ,α∗−kÞ ≥ uðαk, α∗−kÞ under the conditions that k’s contributiondegree increases. Both of the conditions indicate that any kcannot improve the utility by lying the transaction fee bid.Moreover, the attribute of incentive compatibility indicatesthat k satisfies the current transaction fee bid under certainconditions, so that the incentive of the lying transaction feebid is deprived.

4. Problem Description

In this section, we formalize the transaction confirmingproblem in detail to lay the foundation for the establishmentof the UCWTP mechanism, and the basic parametersinvolved in the problem are listed in Table 1.

Assume there are n nodes in the blockchain network anddenoteU as the set of nodes, written asU = f1, 2,⋯, ng. Andthere are two types of roles involved in the transaction con-firming process, respectively, miner m who wins the miningcompetition during the current round and user coalitionCLk, andCLk ∈U ,m ∈U .

According to the real situation of blockchain, there isonly one m who is verified to be valid for packing transac-tions into a new created block to gain the transaction feesduring each round of mining competition. Because the usercoalition k’s actual payment is affected by the discount factorin different priority ranks, in order to ensure the profit ofminer m, m can set the unit reserve price cm for transactionspacked into a new block according to the actual mining cost.User coalition transaction volume, estimated ranking dis-count, and cm are reported to the mechanism by m.

Assume there are ∣CLk ∣ user coalitions in the whole net-work and each user coalition is required to submit the trans-action report which contains transaction informationincluding transaction fee bid set Bk = ½b1, b2,⋯, bk� andtransaction size set Sk = ½s1, s2,⋯, sk�. Denote the report sub-mitted by user coalition CLk as a triple Reqk = ðVk, Bk, SkÞ,where jBkj represents the total volume of transactions in theset due to the arbitrary bid corresponding to a certain trans-action, and Vk represents k’s valuation on the transactions,and Vk also can represent the maximum price k is willingto pay:

Vk =v1, v2,⋯, vn½ �, Sk ≠ 0,0, Sk = 0:

(ð1Þ

The blockchain transaction confirming processing isshown in detail in Figure 1; firstly, users join the coalitionand report the transaction information to the UCTPMmech-anism; miner m who wins the mining competition reportshis/her own information as well; then, the transaction prior-ity ranking results are available according to the UCTPMmechanism. The winning user coalition needs to make thepayment according to the priority ranking results; thus, theessence of the UCWTP algorithm can be seen as to determinethe winner set whose transaction sets are packed into a newblock. Lastly, m gains the total transaction fees paid by win-ning user coalitions and broadcasts the new block to thenetwork.

5. Design of UCTPM Mechanism

Our UCTPMmechanism consists of the UCWTP model andthe TPRP model. The UCWTP model determines the winnerdetermination problem, that is, determining whose transac-tion sets are packed into the new block, while the TPRPmodel is used for the actual payment of winning usercoalitions.

5.1. UCWTP Transaction Priority Model. Assume that thearbitrary user is involved in the blockchain participant inthe activities such as transaction creation, transaction verifi-cation, and extending the main chain, and these historicalactivities are recorded, so that such information can be usedas a basis for calculating the quality score of the user coali-tion. Besides, the user coalition contribution degree and validtransaction volume are also considered the influencing fac-tors for the user coalition quality score in our model, andthe quality score calculation model is as follows:

φk = ϕ0 + conk 〠n

m=1txkmj jð Þ

!μ

: ð2Þ

Table 1: Basic parameters used in this paper.

Notation Explanation

CL Set of user coalition

αk Transaction type demand

Bk Transaction fee bid from user coalition

φk User coalition quality score

Vk Transaction valuation from user coalition

conk User coalition contribution degree

pk User coalition actual payment

uCLk User coalition utility

Sk Transaction set size

θjk The discount factor of k in rank j

4 Wireless Communications and Mobile Computing

In equation (2), ϕ0 is the initial quality score for arbitraryuser coalition k and ϕ0 is a constant value. jtxkmj representsthe valid transaction volume of k during the transactionconfirming processing for the current round (for example,the nth round), which can be divided into two parts pre-cisely: firstly, the total volume of transactions that havebeen recorded into the main chain during the n − 1rounds; secondly, the verified transaction volume for cur-rent round n. And μ is the constrained parameters where0 < μ < 1. In addition, conk is k’s contribution degree andcan be formulated as

conk =1n

〠n

m=1Ωkm × Pkm + 1ð Þ

!: ð3Þ

In equation (3), Ωkm represents the number of transac-tions verified by k at the mth round of transaction con-firming processing, and denote Pkm = f0, 1g to indicatewhether there are users in the coalition who wins the min-ing competition at the mth round, where Pkm = 1 meansthere is such a miner, Pkm = 0 otherwise.

Except for user coalition quality φk which can affect theresults of transaction priority ranking, the different transac-tion types created by k should influence the ranking resultsas well. User coalition can implement different functionsand achieve various purposes by creating various transac-tions, and we roughly divide the common transaction typesinto five categories: transactions with or without lock-time,also with the smart contract operation, creation, and othertransaction types:

typet ⟵ type1, if transaction with lock-time,typet ⟵ type2, if transaction without lock-time,typet ⟵ type3, if creation of smart contract,typet ⟵ type4, if operation of smart contract,typet ⟵ type5, if others.

Considering that the volume of a certain transaction typein the total volume that transactions are recorded on themain chain can reflect the demand degree of this certain typeof transaction, thus we formula the transaction type demanddegree based on typet for arbitrary user i from k as

γi = 1 + ∑ typetj jNum

� �1/ε: ð4Þ

In equation (4), typet reflects the total volume of this cer-tain transaction type recorded on the main chain, Num rep-resents the overall transaction volume on the main chain,and parameter 1/ε help to prevent the boost increase of cer-tain transaction types in the blockchain network fromseverely impacting transaction priority ranking results.Because we consider the scenario that users join the coalitionfor transaction creation, the transaction type demand degreefor k is developed on the average value of equation (4) asshown below:

αk =∑i∈CLkγiCLkj j : ð5Þ

The methods that used to reduce the impact of trans-action fee bid Bk on priority ranking results should notonly focus on the introduction of user coalition qualityscore φk but also consider the impact of Bk on the trans-action priority ranking results which should be graduallydecreased when Bk increases under the condition that usercoalition contribution degree conk keep increasing. There-fore, we adopt a new method to calculate the transactionfee bid as the following:

bk′ = Bk × e− σconkð Þ: ð6Þ

The parameter σð0 < σ < 1Þ is used to restrain theabrupt attenuation of bk′ when conk increases. In addition,

User coalition

Informationcollection

Priorityranking

Winnerdetermination Payment

Payment Report

Report PayoffReport Payoff

Miner

BlockchainExtent themain chain

Figure 1: Basic transaction process diagram of blockchain.

5Wireless Communications and Mobile Computing

only the transaction sets that meet the requirement Bk/jBkj ≥ cm can be processed in order to guarantee the profitof m, where cm is unit reserve price for m. In consequence,we proposed the UCWTP calculation model based onequations (2), (5), and (6):

Bk′ =bk′ × φk × αk

Sk: ð7Þ

The new transaction priority ranking results for usercoalition can be sorted as B1′ ≥ B2′ ≥⋯≥ Bk′ according toequation (7), and the corresponding priority rank is r1 ≥r2 ≥⋯≥rk. Meanwhile, m is supposed to pack the transac-tion sets into a new created block by the rank from highto low until the block size cap. And denote xck = f0, 1gto indicate the transaction set packing results, xck = 1means the transaction set is packed into the new block,and xck = 0 otherwise, so that the winning user coalitionset can be denoted as W = f∀k ∈ CLk ∣ xck = 1g.5.2. TPRP Pricing Model. The user coalition can obtain differ-ent transaction priority ranks by the comprehensive resultsof transaction fee bid, contribution degree, quality scores,and transaction type demand degree, and the actual paymentof the winning user coalition based on various ranks is differ-ent, which also should be irrelevant to the user coalitiontransaction fee bid; otherwise, the user coalition will alwayshave the incentive to lie the transaction fee under the situa-tion of becoming the winner. Thus, we propose the TPRPpricing model that is based on the transaction priority ranksand on the purpose of depriving the correlation between pay-ment and user coalition owning transaction fee bids:

pk = θ jk × Bkj j × cm: ð8Þ

In equation (8), jBkj is the volume of transactions createdby user coalition, and θjk is the discount factor of k when k

ranks j, and also, θjk ≤ θgk when rj ≥ rg:

θ jk = β × rjk ⟶ 0, 1ð �: ð9Þ

The transaction set of winning user coalition is processedby m; then, m broadcasts the new block to the whole block-chain network after the selected transaction sets are packedinto the new generated block; then,m receives the total trans-action fees from winning user coalitions as a reward:

prom = −〠k∈W

pk ð10Þ

The winning user coalition will also be profit after thenew block is considered to be valid as it appended onto themain chain; therefore, the expected revenue Vk is obtainedby k, and the utility of such a user coalition can be formu-lated as

uCLk = xck Vk − pkð Þ: ð11Þ

6. Algorithm and Attribute Proof

6.1. UCWTP Algorithm and TPRP Algorithm. The UCTPMmechanism proposed in this paper mainly includes twoparts: the transaction priority ranking algorithm and the win-ing user coalition pricing algorithm. The essence of the trans-action priority ranking algorithm is used for winnerdetermination so that the specific miner needs to pack theselected transaction sets into the new created block, and thetransaction priority ranking algorithm is called the UCWTPalgorithm, while the TPRP algorithm is the solution to thewinning user coalition payment issue.

Algorithm 1 describes the process of winner determina-tion, and we set each round of priority ranking process asstatic; that is, once the transaction sets are selected for thetransaction priority ranking process, these sets are notaffected by any changes due to new transaction sets arrivingin the mempool. First of all, Steps 2 to 5 indicate that thetransaction priority ranking result of the selected user coa-lition is calculated based on the coalition quality score,transaction type demand degree, transaction fee, and con-tribution degree; Step 7 shows that the new transactionsequence is sorted in a nonincreasing order; finally, Steps8 to 11 determine the winning user coalition sets accordingto the priority ranking result and the block capacitylimitation.

Algorithm 2 describes the pricing process for the winninguser coalition; Steps 2 to 6 illustrate that these user coalitionneeds to make the actual payment according to the transac-tion priority ranking result and the transaction volume, sothat the user coalition actual payment is irrelevant to usercoalition own transaction fee bid. In addition, the lowerthe rank is, the higher the user coalition payment wouldbe due to the discount factor; nevertheless, when the usercoalition wants to lower the actual payment by reachingthe higher transaction priority rank, the user coalition willprefer to improve the unit quality score instead of the unittransaction fee. As a result, it deprives the motivation forthe user coalition to improve utility by lying the transactionfee bid.

6.2. Attribute Proof

(1) If the lower bid bk′ results in the failure of the transac-tion set being packed into the new block, then xck = 0according to equation (11); thus, uCLk′ = 0

(2) If the lower bid bk′ results in lower transaction priorityrank r j, then θjk ≥ θ

gk . And the user coalition actual

payment only depends on the transaction priorityrank and the transaction volume and is irrelevantwith the transaction fee bid; that is, when θjk ≥ θ

gk ,

there exists pjk ≥ pgk , so that, uCLk − uCLk′ =Vk – pgk –

ðVk − pjkÞ = pjk – pgk ≥ 0

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Theorem 9. Arbitrary user coalition k cannot improve utilityby lowering the transaction fee bid in the UCTPMmechanism.

Proof. Assume when the user coalition k bids the transactionfee bk to rank rg and obtains the utility uCLk , while the lower

bid bk′ to rank rj and obtains the utility uCLk′ .

Therefore, the conclusion can be reached through theabove analysis that arbitrary user coalition k cannot improveutility by lowering the transaction fee bid in the UCTPMmechanism.

Theorem 10. Arbitrary user coalition k prefers to improveunit quality score instead of unit transaction fee bid toimprove utility when conk increases.

Proof. The user coalition quality score is calculated according

to equation (2): φk = ðϕ0 + conk ∑n

m=1ðtxkmÞÞ

μ

:

When applied substitution as TXk ⟵∑nm=1ðjtxmkjÞ,

then we can get φk = ðϕ0 + conk × TXkÞμ. And deriving φk

to get φk′ðconkÞ = μTXk. As φk is the monotone increasing

function of conk due to jtxkmj ≥ 0 and μ ≥ 0, thus μTXk ≥ 0,so that φk

′ðconkÞ ≥ 0.Besides, the effect of user coalition contribution degree

conk on transaction fee bid Bk can be written as bk′ = Bk ×e−ðσconkÞ according to equation (6).

Same as above, if B⟵ bk′, then B = Bk × e−ðσconkÞ stands,and deriving B to get B′ðconkÞ = −σBke

−ðσconkÞ. For arbitraryk’s transaction fee bid Bk > 0, and conk ≥ 0, σ > 0, thus B′ðconkÞ ≤ 0, so that, bk′ is the monotone decreasing function

Input: Reports submitted by user coalition: Rcl = fr1, r2,⋯, rng, rn = <Vk, Bk, Sk >Reports submitted by miner: Rm = <cm >

Output: W: the sets of winning user coalition1 initialize sum⟵ 0,W ⟵N , L⟵∅C⟵ maximum size of a block2 for all k ∈W do3 bk′ = Bk × e−ðσconkÞ

4 φk = ðϕ0 + conk∑nm=1ðjtxkmjÞμ

5 Bk′⟵ ðbk′ × φk × αk/SkÞ6 end for7 sort W in non-increasing order of Bk′: B1′ ≥ B2′ ≥⋯≥ Bk′8 for all i ∈W do9 if sum ≤ C then10 sum + = Si11 W ⟵W \ fig, L⟵ L ∪ fig12 end if13 end for14 W ⟵∅15 W ⟵ L16 return W

Algorithm 1: UCWTP.

Input: Reports submitted by user coalition: Rcl = fr1, r2,⋯, rng, rn = <Vk, Bk, Sk >Reports submitted by miner: Rm = <cm >W: the sets of winning user coalition

Output: p the payment sets of winning user coalition1 initialize p⟵∅2 sort W in non-increasing order of Bk′: B1′ ≥ B2′ ≥⋯≥ Bk′3 for all i ∈W do

4 pi = θji × jBij × cm5 p⟵ p ∪ pi6 W ⟵W \ fig7 end for8 return p

Algorithm 2: TPRP.

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of conk. And the inequation φk′ðconkÞ ≥ B′ðconkÞ shows

that the priority ranking that arbitrary user coalitionobtains through improving the unit quality score is higherthan improving unit transaction fee bid.

Denote the strategy set of user coalition k as Ak = fα, α′g,where α means the user coalition’s strategy of improvingthe unit quality score, while α′ means the strategy ofimproving the unit transaction fee bid. We only considerthe pure strategy action instead of mixed strategy actionfor simplification; that is, k only chooses one of specificstrategies from strategy set Ak. Denote the utility is uCLkwhen k chooses the strategy of α to obtain the priorityrank rg, while utility is uCLk′ when k chooses the strategy

of α′ to obtain the priority rank r j, thus rg ≥ r j based onthe analysis above. Considering comprehensively withequation (8), it shows that pjk ≥ pgk when θjk ≥ θ

gk , so that

uCLk − uCLk′ =Vk – pgk – ðVk − pjkÞ = pjk – p

gk ≥ 0, which means

arbitrary user coalition will not choose strategy of α′ toimprove the utility. According to the analysis above, theconclusion can be summed up that arbitrary user coalitionk cannot improve utility by improving the transaction feebid in the UCTPM mechanism.

(1) When bk′ < bk, according to Theorem 9, arbitrary khas the utility uCLk − uCLk′ ≥ 0, which means k cannotimprove the utility through lowering transaction feebid

(2) When bk′ > bk, according to Theorem 10, for arbitraryk prefers to improve the unit quality score rather thanunit transaction fee bid for the higher priority rank toimprove utility, which means there is no such a k thatchooses the strategy of improving unit transaction feefor extra utility when the coalition contributiondegree increases

Theorem 11. The UCTPM mechanism satisfies the attributeof incentive compatibility when conk increases.

Proof. Denote the utility of user coalition k is uCLk when k

bids transaction fee bk, while uCLk′ when k bids transaction

fee bk′.

From the analysis of (1) and (2), it can be proved that theUCTPM mechanism satisfies the attribute of incentive com-patibility when conk increases.

(1) When xck = 1, which means the transaction set forthis user coalition is added into the new block,thus uCLk = Vk – pk. And user coalition k’s actualpayment pk is not higher than Bk based on equa-tions (8) and (9), so that pk ≤ Bk. In addition, Vk≥ Bk holds for users who use blockchain as thetransaction platform; otherwise, they prefer the

off-chain methods. Therefore, the utility of kis uCLk = xckðVk – pkÞ =Vk – pk ≥ 0

(2) When xck = 0, which means the transaction set of k isnot appended onto the main chain, and also, there isno need for such a k to pay, so that uCLk = 0

Theorem 12. The UCTPM mechanism satisfies the attributeof individual rationality.

Proof. The user coalition k’s utility is written as uCLk = xckðVk – pkÞ according to equation (11).

The conclusion can be summarized from the analysisabove that the UCTPM mechanism is individual rationalaccording to analyses (1) and (2).

Theorem 13. The UCTPM mechanism satisfies the attributeof budget balanced.

Proof. According to the payment function defined by theUCTPM mechanism for winning user coalition and miner,the sum of all participants in the mechanism is zero; that is,prom +∑k∈Wpk = 0; thus, the UCTPM mechanism satisfiesthe attribute of budget balanced.

7. Experiment

The simulation experiment codes are implemented in Pythonlanguage, and the test hardware is Intel® Core™ i5-4200UCPU+4GBmemory, andWindows 10+Python 3.7+Pycharm2019 are used for the test software. We conduct the simula-tion experiments to mainly explore two contents based onthe researches in this paper: Firstly, the transaction priorityranking results influenced by the UWCTP algorithm areexplored. Secondly, the influences of the UCTPM mecha-nism on transaction processing time are explored. The exper-imental results show the feasibility and effectiveness of theUWCTPmechanism, and the detailed experimental contentsare as follows:

(1) Exploring the influence of the increasing transactionfee and valid transaction volume on transaction pri-ority scores as user coalition contribution degreeincreases

(2) Observing the influence differences of the UCWTPalgorithm and traditional transaction priority algo-rithm on transaction priority ranking results

(3) Exploring the transaction processing time differencescaused by different transaction creation modes(transactions created by a single user and user coali-tion) under different transaction volumes in themempool

In order to explore the influence of the increasing trans-action fee bid and valid transaction volume on priorityresults, we generate the transaction fee within the range of

8 Wireless Communications and Mobile Computing

[0, 3]/BTC based on the real Bitcoin situation [24] and gen-erate the valid transaction volume within the range of [1,1000] on the basis of assuming that the maximum validtransaction volume is 1000 in the experimental situation. Inall the experiments, the random number generator of Pythonis used to generate the experimental data, and the averagenumber is applied after the experimental data are generated500 times with the purpose of reducing the influence of ran-domness on experimental results. From Figure 2, it can beobserved that the priority score corresponds to the increasingtransaction fee bid which goes up first, then drops down andtends to 0 as the contribution degree increases with the stepof 5, and the results about the transaction fee influence on

priority score under different sets of σ share the same ten-dency. Meanwhile, we conduct the other experiment aboutthe influence of increasing valid transaction volume on thepriority score. As the result shows in Figure 3, the overall pri-ority score goes up as the contribution degree increases;besides, the upward trend becomes faster when μ is higher.Moreover, as the value range of the transaction fee is muchsmaller than the valid transaction volume, there is a huge dif-ference in the score result value, but the result comparisonwill not be affected; instead, the result value difference indi-cates that when user coalition increases transaction volumerather than transaction fee bid, the significant higher priorityscore will be obtained.

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Figure 3: Influence of valid transaction volume on priority score.

9Wireless Communications and Mobile Computing

In order to make further impact comparisons of theUCWTP algorithm and traditional transaction priority algo-rithm on the priority ranking results, we conduct the secondexperiment as the result shows in Figure 4, and we randomlygenerate 500 transaction fees in the range of [0, 80]/BTC asthe user coalitions’ transaction fee bid to imitate the actualBitcoin transaction situation as possible. As it shows inFigure 4, the transaction fee bid is linearly related to thetransaction priority degree under the traditional transactionpriority algorithm; as a result, user coalition can obtain ahigher transaction priority rank through improving transac-tion fee bid directly. However, with the UCWTP algorithm,the user coalition quality score increases with the growth ofvalid transaction volume of the user coalition, and the influ-ence of single transaction fee on the transaction prioritydegree is reduced by an average of 2.34%, and it can bereduced by up to 12.2%; this is mainly because the rankingdeviation obtained by the UCWTP algorithm will be reducedwhen the transaction fee of user coalition is low. However, itis interesting to notice that the impact of a single transactionfee on the priority degree is reduced by an average of 5.17%when referring to the annual ratio of approximately 21.66%for Bitcoin transaction packing (that is, the annual averageratio of the confirmed transactions to the total number oftransactions in the blockchain platform from April 2019 toApril 2020 [19]).

The experiment results above are consistent with the con-clusion of Theorem 10; it is further proved that the arbitraryuser coalition can obtain a higher transaction priority rankthrough improving the quality score when the coalition con-tribution degree increases; thus, the user coalition prefers toimprove the quality score rather than lying to improve thetransaction fees on the purpose of optimizing the utility.Besides, the experiment results reflect that the UCTPMmechanism can effectively incentivize users in coalitions toactively participate the blockchain’s activities includingtransaction creation, transaction verification, competition

for bookkeeping right, and other activities that help toimprove coalition quality scores and contribution degree;sequentially, we believe that the development of the block-chain can be helped to promote in the long run by adoptingthe UCTPM mechanism.

In addition to the two experiments we conducted forexploring the impacts of the UCWTP algorithm on transac-tion priority ranking results, we also implement the experi-ment on transaction confirming process time with thedifferent transaction creation modes. In detail, we set uptwo different transaction creation modes to conduct the con-trast experiments based on the researches in this paper,which are transactions created by a single user and by usercoalitions, respectively. Also, the increment step of transac-tion volumes is set up as 5000 and end up by 60000 in thisexperiment. Although when compared with the transactionvolume in the real Bitcoin situation, the experimental trans-action volume is smaller, the experimental results as shownin Figure 5 can still reflect that the overall transaction con-firming process time for the transactions created by user coa-lition is much faster than transactions created by a singleuser. Under the condition of the increased transaction vol-ume, the transaction processing time of transactions createdby a single user grows faster than that of transactions createdby user coalition, and the maximum difference in transactionprocessing time between these two transaction creationmodes is up to 6.9347 s when transaction volume reaches60000. From the transaction processing time growth trendof Figure 5, we predict that if the UCTPMmechanism wouldbe operated in the real blockchain project such as Bitcoin, theoverall transaction confirming process time could be signifi-cantly reduced with the help of the UCTPM mechanism,because the user coalition transaction creation mode helpsto effectively reduce the total time it takes miners to decidewhich transaction should be packed into a new block underthe condition that no other factors affecting transaction con-firming process time should be taken into consideration.

500

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y de

gree

100

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0 10 20 30 40Transaction fee/BTC

Priority degree under traditional ranking algorithmPriority degree under UCWTP algorithm

50 60 70 80

Figure 4: Impact of valid transaction volume and transaction fees on priority degree.

10 Wireless Communications and Mobile Computing

8. Conclusion and Future Work

Considering the issues of single-user transaction creationmodes and limited influence factors on transaction priorityalgorithms in the current blockchain research fields, we pro-pose a novel pricing mechanism called the UCTPM mecha-nism to optimize the traditional transaction priorityalgorithm and enrich the transaction creation modes. Inaddition, the user coalition quality score, user coalition con-tribution degree, and transaction type demand degree areintroduced into the UCTPM mechanism to reduce theimpact of the transaction fee on transaction priority rankingresults.

In our proposed UCTPM mechanism, it is provedthrough theoretical proof and experimental analysis thatthe UCTPM mechanism can deprive the motivation of usercoalition lying the transaction fees for extra utility as the usercoalition contribution increases. From the aspect of theUCWTP algorithm, it demonstrates that the UCWTP algo-rithm can help to reduce the impacts of transaction fees onthe transaction priority ranking results by an average of5.17%, and the impacts can be reduced by up to 12.2% whencompared to the traditional transaction priority rankingalgorithm. While in terms of the performance of the UCTPMmechanism, the transaction confirming process time isgreatly shorter when the transactions are created by user coa-lition instead of individual users from our related experimentresults; it is also confirmed from the theoretical proof that theUCTPMmechanism satisfies the attributes of incentive com-patibility, individual rationality, and budget balanced.

Although the outcomes of the researches conducted bythis paper provide a new approach for the transaction prior-

ity ranking in blockchain, also enriching the modes of usertransaction creation, the calculation models of unit reserveprice for the miner who is granted the bookkeeping right,and the discount factor when the user coalition reaches cer-tain ranks is not formalized in detail; thus, our future workwill focus on the dynamic unit reserve price and discount fac-tor formalization based on the actual blockchain transactionsituation.

Data Availability

The (experimental data) data used to support the findings ofthis study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China under Grant 61872313, in partby the Key Research Projects in Education Informatization inJiangsu Province under Grant 20180012, in part by the Post-graduate Research and Practice Innovation Program ofJiangsu Province under Grant KYCX18\_2366, in part bythe Yangzhou Science and Technology Bureau under GrantsYZ2018209 and YZ2019133, in part by the Yangzhou Uni-versity Jiangdu High-End Equipment Engineering Technol-ogy Research Institute Open Project under GrantYDJD201707, and in part by the Open Project in the State

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Figure 5: Transaction processing time differences between different transaction creation modes.

11Wireless Communications and Mobile Computing

Key Laboratory of Ocean Engineering, Shanghai Jiao TongUniversity, under Grant 1907.

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