Evolutionary Game Analysis for the Regulation of Merchants Selling Counterfeits on E-commerce Platforms

: In recent years, the phenomenon of merchants selling counterfeits has occurred frequently, exposing the lack of supervision by government and e-commerce platforms. In order to solve the problem of merchants selling counterfeits on e-commerce platforms, this paper takes the governments, e-commerce platforms and consumers as the regulatory participants, building a tripartite evolutionary game model, obtaining the system evolutionary equilibrium point, analyzing the equilibrium point and its stability, and finally providing corresponding countermeasures and suggestions for the supervision of merchants selling counterfeits on e-commerce platforms.


Introduction
With the rapid development of the Internet, the network economy dominated by e-commerce is changing the traditional business model.Online shopping has a blowout growth, and e-commerce platforms are playing an important role in promoting e-commerce.However, the phenomenon of merchants selling fake goods has also become increasingly prominent.
The problem of merchants selling counterfeits has always been a hot topic of research, and scholars at home and abroad have conducted in-depth research on it.Most scholars believe that it is mainly caused by information asymmetry, consumers cannot grasp quality information like merchants [1], and e-commerce platforms have low threshold for merchants, weak platform supervision, and low cost for merchants to sell fake goods [2][3].The cost of supervision and the intensity of punishment are very important factors influencing the supervision of sellers selling counterfeits.Reducing the cost of supervision and increasing the intensity of punishment can effectively solve the problem of merchants selling fake goods [4][5].In addition, it is not enough to rely only on the supervision of a single subject, which requires the participations of multiple parties such as the governments and e-commerce platforms.Zhang analyzed the game of product quality supervision between e-commerce platforms and product producers [6].Si took the genuine manufacturers and the counterfeit enterprises as game players and analyzed that government-enterprise cooperation mechanism can crack down on counterfeit behaviors [7].
To sum up, in terms of the regulation of sellers' counterfeit behaviors, few scholars have considered the dynamic game among the governments, e-commerce platforms and consumers, as well as the influence of different conditions on the regulation of merchants' counterfeit behaviors.Therefore, this paper constructs an evolutionary game model to analyze the strategy choices of participants in the regulation of merchants selling counterfeits under different circumstances.

Basic assumptions of the model
In the supervision mechanism of merchants selling counterfeits on e-commerce platforms, this paper sets up three participants: government, e-commerce platform and consumer.The logical relationship of the game model constructed in this paper is as follows: Assumption1：All three players are limited rationality; when one player makes a strategy adjustment, the other players will make the adjustment simultaneously.
Assumption2: Government is player 1, e-commerce platform is player 2, and consumer is player 3. players all adopt two strategies and make decisions independently of each other.The strategy set of the government is {supervision, non-supervision}, and the probability is (0 1) x x   , and 1 x  , respectively.The strategy set of e-commerce platforms is {constraint, non-constraint} and the probability is (0 1) y y   , and 1 y  , respectively.The strategy set of consumer is {feedback, non-feedback} and the probability is (0 1) z z   , and 1 z  , respectively.

2.2Model construction
Based on the principle of profit maximization, all participants will make the best decision.In supervision mechanism of merchants counterfeiting, the e-commerce platform is responsible for restraining merchants selling counterfeits, supervising the quality of products sold by merchants, and handling consumers' complaints against merchants.If e-commerce platform fails to fulfill its duty, it will be punished by government.This paper summarizes the variables and parameters used to construct the tripartite game model, which is shown in table 1.Based on the above basic assumptions and the variables and parameters in table 1, this paper constructs the tripartite payoff matrix of the government, e-commerce platform and consumer.The payoff matrix is shown in table 2.

R
Additional earnings of restraint strategy adopted by the e-commerce platform.
2 R Additional earnings of non-restraint strategy adopted by the e-commerce platform.

P B
Government incentives of restraint strategy adopted by the e-commerce platform.

p C
The cost of restraint strategies adopted by e-commerce platform.
p F Punished by government of non-restraint strategy adopted by the e-commerce platform.
p D Reputation loss caused by consumer complaints when e-commerce platforms adopt unconstraint. 1

M
The value of information obtained by consumers when the government releases sampling inspection results and trustbreaking lists on the regulatory information platform. 2

M
The value of information obtained by consumers when the e-commerce platforms publish merchants reputation and review results on regulatory information platforms.

M
The value of information obtained by consumers when government regulatory departments and third-party ecommerce platform release information at the same time.
The dynamic replication equations of the government, e-commerce platforms and consumers are as follows:

Evolutionary stability strategy analysis
The stability analysis of equilibrium point in tripartite evolutionary game can be judged according to Lyapunov indirect method.To further obtain the stable equilibrium point, Jacobian matrix is used for analysis.
According to Lyapunov indirect method, if matrix eigenvalues are all less than 0, then the point is evolutionary stable strategy, namely ESS.If there are positive eigenvalues, it is an unstable point.Combined with the existing conditions, the analysis of equilibrium points is divided into case 1 (R 1 -R 2 -C p >0) and case 2 (R 1 -R 2 -C p <0).The results are shown in table 3.
Under certain conditions, the evolutionary game for regulation system of merchants counterfeiting reaches a stable state.There are four evolutionary stable strategies.
In case 1, the e-commerce platform will earn more if it restrains merchants from selling counterfeits, and the system may have an evolutionary stability point of (0,1,0) or (1,1,0).When these parameters satisfy condition 1, the eigenvalues of (0,1,0) are all negative value, so the ESS is (1,1,0).Similarly, when parameters satisfy conditions 2, the evolutionary stability point of the system is (1,1,0).

Conclusion
From the perspective for regulation of merchants selling counterfeits, this paper constructs a game model with the government, e-commerce platform and consumer, and analyzes the stability of each player's strategy selection, and draws the following conclusions: Government should establish reward and punishment mechanism.The government will incentivize those ecommerce platforms that find fraud, and impose heavy fines on those platforms that connive at fraud.
Cost also influence the strategic choice of government and e-commerce platforms.In order to reduce the cost of supervision, supervision information system should be established to realize real-time supervision.
In addition, high compensation and low feedback costs will encourage consumers to choose feedback as an evolutionary stable strategy.The punishment of merchant fraud should be increased and the protection of consumers should be strengthened.
Based on the research, this paper believes that the government and e-commerce platforms can effectively regulate the counterfeit selling behavior of merchants to a certain extent and promote the development of ecommerce platforms.

L
Losses incurred by consumers receiving fake goods.G E-commerce platform compensation when consumers successfully complain.

Table 1 .
The meaning of the variables and parameters in the tripartite game model Symbols Description g PSocial benefits of regulation strategy adopted by the government.gCRegulationcost of regulation strategy adopted by the government.gFPunishedbysuperior departments of non-regulation strategy adopted by the government.RBasic income of daily operation of e-commerce platform.1

Table 2 .
The tripartite payoff matrix for the regulation of merchants selling counterfeits

Table 3 .
Stability analysis of equilibrium point of game system