Express package recovery subject enthusiasm game analysis method under reward and punishment mechanism

Abstract

The invention relates to the technical field of express package recovery, and discloses an express package recovery subject enthusiasm game analysis method under a reward and punishment mechanism. Building a government-recoverer-consumer three-party evolutionary game model; copying a dynamic equation and analyzing an evolution equilibrium point; according to an evolutionary game theory and a Lyapunov system stability discrimination method, carrying out tripartite evolutionary game equilibrium point stability analysis; through MATLAB numerical simulation analysis, the influence of the initial probability on the evolution path of the tripartite game body and the influence of different factors on the evolution path of the tripartite game body are obtained. From the perspective of evolutionary game, a government reward and punishment mechanism is introduced into an income matrix, a government-recoverer-consumer three-party game model under the government reward and punishment mechanism is constructed, and the evolutionary process of different parameter changes on government, recoverer and consumer behaviors is analyzed. Therefore, reasonable suggestions are provided for promoting healthy, stable and orderly development of the express package recovery industry.

Description

Technical Field

[0001] The present invention relates to the technical field of express packaging recycling, and in particular to a game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism. Background Art

[0002] The current recycling rate of express packaging has not reached 20%, and the recycling rate of cartons and other supplies used in express delivery has not exceeded 10%. More than 70% of users treat express packaging as "garbage" after unpacking it. The contrast between the large-scale use of express packaging and the recycling rate of less than 10% has led to a sharp consumption of resources used to manufacture express packaging and increased pressure on environmental protection. The recycling and reuse of express packaging requires the systematic participation of all parties, but the interests of all parties are different, and the conflicts between them may become an important reason hindering the development of green packaging. Due to the differences and conflicts in the demands of different stakeholders, all parties must actively participate in the green recycling of express packaging.

[0003] Previous studies have mostly focused on the analysis of government financial subsidies, tax incentives, and the behaviors of various participating entities, and have studied the game between "express delivery companies-consumers", "government-e-commerce companies" and "e-commerce companies-consumers" respectively. However, few studies have considered that the express packaging recycling industry is the result of joint promotion by the government, recyclers, and consumers. There are even fewer studies on the enthusiasm of the participating entities. Government supervision and punishment are the means to ensure the healthy development of the express packaging recycling industry, which has led to an imperfect theoretical research system on the enthusiasm of the participating entities in express packaging recycling, resulting in an uneven distribution of interests among all parties, affecting the recycling of express packaging, and having a significant impact on the environment, industry development, and consumers. Therefore, a game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism is proposed to solve the above-mentioned problems. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the shortcomings of the prior art, the present invention provides a game analysis method for the enthusiasm of express packaging recycling subjects under a reward and punishment mechanism, which has the advantages of enriching and supplementing the theoretical research system of the enthusiasm of express packaging recycling participants, broadening the application field of evolutionary game and enriching the research model in the field of the enthusiasm of express packaging recycling participants. It solves the problem that the theoretical research system of the enthusiasm of express packaging recycling participants is not perfect due to previous theoretical research, resulting in uneven distribution of interests among all parties, affecting the recycling of express packaging, and causing a great impact on the environment, industry development and consumers.

[0006] (II) Technical solution

[0007] In order to achieve the above-mentioned purpose of enriching and supplementing the theoretical research system of the enthusiasm of the participants in express packaging recycling, broadening the application field of evolutionary games and enriching the research model in the field of the enthusiasm of the participants in express packaging recycling, the present invention provides the following technical solutions: a game analysis method for the enthusiasm of express packaging recycling participants under a reward and punishment mechanism, comprising the following steps:

[0008] Step 1: Model assumptions and parameter settings, and make the following assumptions:

[0009] 1) The three parties involved in the game, recyclers, consumers and the government, are all bounded rational participants. Under bounded rationality conditions, each player often cannot find their own optimal strategy at the beginning, but adjusts their own strategy based on experience;

[0010] 2) In the recycler-consumer-government evolutionary game model, the recycler's strategy choices include active recycling and passive recycling, the consumer's strategy choices include active participation and passive participation, and the government's strategy choices include implementing a reward and punishment mechanism and not implementing a reward and punishment mechanism. x, y, and z are used to represent the probability that the recycler actively recycles, the consumer actively participates in the recycling of express packaging, and the government implements an active regulatory strategy, and 0<x, y, z<1;

[0011] 3) When only one party, recyclers or consumers, actively participates in the recycling of express packaging, the party that passively participates in recycling can obtain additional benefits through "free-riding" behavior.

[0012] Step 2: Construct the government-recycler-consumer three-party evolutionary game model and set up the corresponding matrix;

[0013] Step 3: Replicate the dynamic equation and analyze the evolutionary equilibrium point, including the evolutionary equilibrium analysis of recyclers, consumers and government decision-making;

[0014] Step 4: Based on the evolutionary game theory and Lyapunov system stability judgment method, conduct stability analysis of the equilibrium point of the three-party evolutionary game;

[0015] Step 5: Through MATLAB numerical simulation analysis, we can obtain the influence of initial probability on the evolution path of the three-party game subject and the influence of different factors on the evolution path of the three-party game subject.

[0016] Preferably, the active recycling of the recyclers is reflected in the research and development of recycling technology, investment in and improvement of facilities and equipment, etc., and the active participation of the consumers is reflected in the correct classification, collection and transportation of waste to recycling companies.

[0017] Preferably, the implementation of the reward and punishment mechanism strategy mainly refers to the government regulatory authorities using the reward and punishment mechanism to give rewards and subsidies to consumers and recyclers who actively participate in recycling, and to punish recyclers who passively participate in express packaging recycling.

[0018] Preferably, in step one, the benefits allocated to recyclers and consumers for actively participating in the recycling of express packaging should be greater than the benefits they obtain through "free riding", that is, it is assumed in this article that ω1M>R1λq, ω2M>R2λq.

[0019] Preferably, ω1M>R1λq,ω2M>R2λq, wherein:

[0020] R1: The unit recycling income of the recycler for the express packaging;

[0021] C1: The unit recycling cost of express packaging by recyclers, mainly including unit recycling price, human resource costs, facilities and equipment input costs;

[0022] R2: Unit recycling revenue of consumers recycling express packaging;

[0023] C2: The unit recycling cost of express packaging by consumers, mainly including the time cost invested, etc.

[0024] q: The amount of recycled express packaging;

[0025] α1: The degree of efforts made by recyclers to actively participate in recycling, mainly referring to the research and development of recycling technology, investment and improvement of facilities and equipment, etc., 0<α1<1;

[0026] α2: The degree of effort of consumers to actively participate in recycling, mainly referring to the correct classification, collection, and transportation of waste to recycling companies, etc., 0<α2<1;

[0027] K1: The recycler’s own capability level;

[0028] K2: Consumers’ own ability level;

[0029] M: Additional revenue created when both recyclers and consumers actively participate in recycling;

[0030] ω1: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to recyclers, 0<ω1<1;

[0031] ω2: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to consumers, 0<ω2<1;

[0032] λ: When only one party, the recycler or the consumer, actively participates in recycling, the unit profit increase rate that the party that passively participates in recycling can obtain additional benefits through "free riding" behavior;

[0033] γb: The negative recycling behavior of recyclers leads to a decrease in market share expectations and consumer dissatisfaction γ (0<γ<1);

[0034] βS: When the government implements the reward and punishment mechanism, it gives financial subsidies to recyclers with positive attitudes, and the subsidy intensity is β, 0<β<1;

[0035] When the government implements a reward-penalty mechanism, the penalty imposed on recyclers who adopt a negative attitude is the intensity of supervision φ (0<φ<1);

[0036] A: When the government implements a reward and punishment mechanism, it rewards consumers who actively participate in recycling;

[0037] F1: The benefits gained from the improvement of the government’s image and social credibility when it implements a reward and punishment mechanism;

[0038] F2: Recyclers and consumers actively participate in the express packaging recycling industry chain. The express packaging recycling and reuse industry is developing well, with obvious effects on environmental improvement. The government (local government) has received awards from higher-level governments.

[0039] C3: administrative costs incurred when the government implements the reward and punishment mechanism;

[0040] J: When the government does not implement a reward and punishment mechanism, and when recyclers and consumers adopt a passive strategy, the packaging recycling and reuse industry lags behind, leading to worsening environmental pollution and punishment from higher-level governments on the government (local government);

[0041] N: When the government does not implement a reward and punishment mechanism, recyclers and consumers will lose their sense of dependence and trust in it, which will bring adverse effects to themselves.

[0042] Preferably, the matrix in step 2 includes:

[0043] 1) The three-party game profit matrix of recyclers actively recycling under the government (z) implementation of the reward and punishment mechanism;

[0044] 2) The three-party game profit matrix of recyclers’ passive recycling under the government (z) implementation of the reward and punishment mechanism;

[0045] 3) The three-party game profit matrix of recyclers actively recycling when the government (1-z) does not implement a reward and punishment mechanism;

[0046] 4) The three-party game profit matrix of recyclers’ passive recycling when the government (1-z) does not implement a reward and punishment mechanism.

[0047] Preferably, in the evolutionary equilibrium analysis of the recycler, for the recycler, assuming that the expected return of the recycler who chooses the active recycling strategy is U1, the expected return of the recycler who chooses the passive recycling strategy is U2, and the average expected return is U, the replication dynamic equation of the recycler's strategy selection is F(x), and the expression is as follows:

[0048]

[0049] U=xU1+(1-x)U2,

[0050] The replication dynamic equation for the recycler strategy selection is:

[0051]

[0052] Preferably, the evolutionary equilibrium analysis of the consumer, for the consumer, assume that the expected return of the consumer choosing the active recycling strategy is S1, the expected return of the consumer choosing the passive participation strategy is S2, the average expected return is S, and the replication dynamic equation of the consumer strategy selection is F(y), which is expressed as follows:

[0053] S1=xz[(R2-C2)q+ω2M+A-α2K2]+(1-x)z[(R2-C2)q+A-α2K2]

[0054] +x(1-z)[(R2-C2)q+ω2M-α2K2]+(1-x)(1-z)[(R2-C2)q-α2K2]

[0055] =xω2M+zA+(R2-C2)q-α2K2

[0056] S2=xz[R2(q+λq)-C2q]+(1-x)z(R2-C2)q+x(1-z)[R2(q+λq)-C2q]

[0057] +(1-x)(1-z)(R2-C2)q

[0058] =xR2λq+(R2-C2)q

[0059] S=yS1+(1-y)S2

[0060] The replication dynamic equation for consumer strategy selection is:

[0061]

[0062] Preferably, in the evolutionary equilibrium analysis of government decision-making, for the government, assuming that the expected benefit of the government's choice to implement the reward and punishment mechanism strategy is W1, the expected benefit of not implementing the reward and punishment mechanism is W2, the average expected benefit is W, and the replication dynamic equation of the government's strategy selection is F(z), which is expressed as follows:

[0063]

[0064] W2=xy(F2-N)+x(1-y)(-N)+(1-x)y(-N)+(1-x)(1-y)(-JN)

[0065] =xJ+yJ+xy(F2-J)-JN

[0066] W=zW1+(1-z)W2

[0067] The replication dynamic equation for government strategy selection is:

[0068]

[0069] (III) Beneficial effects

[0070] Compared with the prior art, the present invention provides a game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism, which has the following beneficial effects:

[0071] 1. The game analysis method of the enthusiasm of express packaging recycling entities under the reward and punishment mechanism introduces the government reward and punishment mechanism into the profit matrix from the perspective of evolutionary game, constructs a government-recycler-consumer three-party game model under the government reward and punishment mechanism, and analyzes the evolution of different parameter changes on the behavior of the government, recyclers and consumers, so as to put forward reasonable suggestions for promoting the healthy, stable and orderly development of the express packaging recycling industry.

[0072] 2. The game analysis method of the enthusiasm of express packaging recycling entities under this reward and punishment mechanism takes into account the "free-riding" behavior of the participating entities in the express packaging recycling process, and introduces rewards and punishments from higher-level governments to local governments. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is a flow chart of the game analysis method for the enthusiasm of express packaging recycling entities under the reward and punishment mechanism of the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] See also Figure 1 , a game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism, including the following steps:

[0076] Step 1: Model assumptions and parameter settings, and make the following assumptions:

[0077] 1) The three parties involved in the game, recyclers, consumers and the government, are all bounded rational participants. Under bounded rationality conditions, each player often cannot find their own optimal strategy at the beginning, but adjusts their own strategy based on experience;

[0078] 2) In the recycler-consumer-government evolutionary game model, the recycler's strategy choices include active recycling and passive recycling, the consumer's strategy choices include active participation and passive participation, and the government's strategy choices include implementing a reward and punishment mechanism and not implementing a reward and punishment mechanism. x, y, and z are used to represent the probability that the recycler actively recycles, the consumer actively participates in the recycling of express packaging, and the government implements an active regulatory strategy, and 0<x, y, z<1;

[0079] Specifically, recyclers include recycling stations, packaging manufacturers, express delivery companies, third-party recycling companies, e-commerce companies, and all other institutions or organizational groups that specialize in recycling or have recycling functions.

[0080] Consumers refer to the consumer group with recycling capabilities, and governments refer to local governments.

[0081] 3) When only one party, recyclers or consumers, actively participates in the recycling of express packaging, the party that passively participates in recycling can obtain additional benefits through "free-riding" behavior.

[0082] Step 2: Construct the government-recycler-consumer three-party evolutionary game model and set up the corresponding matrix;

[0083] Step 3: Replicate the dynamic equation and analyze the evolutionary equilibrium point, including the evolutionary equilibrium analysis of recyclers, consumers and government decision-making;

[0084] Step 4: Based on the evolutionary game theory and Lyapunov system stability judgment method, conduct stability analysis of the equilibrium point of the three-party evolutionary game;

[0085] Specifically, when the eigenvalues ​​corresponding to the equilibrium point of the Jacobian matrix are all negative, then the equilibrium point is an asymptotically stable point; when the eigenvalues ​​have positive values, then the equilibrium point is an unstable point.

[0086] Step 5: Through MATLAB numerical simulation analysis, we can obtain the influence of initial probability on the evolution path of the three-party game subject and the influence of different factors on the evolution path of the three-party game subject.

[0087] exist Figure 1In the recycling process, the active participation of recyclers is reflected in the research and development of recycling technology, investment in and improvement of facilities and equipment, etc., and the active participation of consumers is reflected in the correct classification, collection and transportation of waste to recycling companies.

[0088] It also includes the implementation of the reward and punishment mechanism strategy, which mainly refers to the government regulatory authorities using the reward and punishment mechanism to give rewards and subsidies to consumers and recyclers who actively participate in recycling, and to punish recyclers who passively participate in express packaging recycling.

[0089] In addition, in step 1, the benefits allocated to recyclers and consumers for actively participating in recycling of express packaging should be greater than the benefits they get through "free riding", that is, in this paper, it is assumed that ω1M>R1λq,ω2M>R2λq, where:

[0090] R1: The unit recycling income of the recycler for the express packaging;

[0091] C1: The unit recycling cost of express packaging by recyclers, mainly including unit recycling price, human resource costs, facilities and equipment input costs;

[0092] R2: Unit recycling revenue of consumers recycling express packaging;

[0093] C2: The unit recycling cost of express packaging by consumers, mainly including the time cost invested, etc.

[0094] q: The amount of recycled express packaging;

[0095] α1: The degree of efforts made by recyclers to actively participate in recycling, mainly referring to the research and development of recycling technology, investment and improvement of facilities and equipment, etc., 0<α1<1;

[0096] α2: The degree of effort of consumers to actively participate in recycling, mainly referring to the correct classification, collection, and transportation of waste to recycling companies, etc., 0<α2<1;

[0097] K1: The recycler’s own capability level;

[0098] K2: Consumers’ own ability level;

[0099] M: Additional revenue created when both recyclers and consumers actively participate in recycling;

[0100] ω1: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to recyclers, 0<ω1<1;

[0101] ω2: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to consumers, 0<ω2<1;

[0102] λ: When only one party, the recycler or the consumer, actively participates in recycling, the unit profit increase rate that the party that passively participates in recycling can obtain additional benefits through "free riding" behavior;

[0103] γb: The negative recycling behavior of recyclers leads to a decrease in market share expectations and consumer dissatisfaction γ (0<γ<1);

[0104] βS: When the government implements the reward and punishment mechanism, it gives financial subsidies to recyclers with positive attitudes, and the subsidy intensity is β, 0<β<1;

[0105] When the government implements a reward-penalty mechanism, the penalty imposed on recyclers who adopt a negative attitude is the intensity of supervision φ (0<φ<1);

[0106] A: When the government implements a reward and punishment mechanism, it rewards consumers who actively participate in recycling;

[0107] F1: The benefits gained from the improvement of the government’s image and social credibility when it implements a reward and punishment mechanism;

[0108] F2: Recyclers and consumers actively participate in the express packaging recycling industry chain. The express packaging recycling and reuse industry is developing well, with obvious effects on environmental improvement. The government (local government) has received awards from higher-level governments.

[0109] C3: administrative costs incurred when the government implements the reward and punishment mechanism;

[0110] J: When the government does not implement a reward and punishment mechanism, and when recyclers and consumers adopt a passive strategy, the packaging recycling and reuse industry lags behind, leading to worsening environmental pollution and punishment from higher-level governments on the government (local government);

[0111] N: When the government does not implement a reward and punishment mechanism, recyclers and consumers will lose their sense of dependence and trust in it, which will bring adverse effects to themselves.

[0112] exist Figure 1 In the second step, the matrix includes:

[0113] 1) The three-party game profit matrix of recyclers actively recycling under the government (z) implementation of the reward and punishment mechanism;

[0114]

[0115] 2) The three-party game profit matrix of recyclers’ passive recycling under the government (z) implementation of the reward and punishment mechanism;

[0116]

[0117] 3) The three-party game profit matrix of recyclers actively recycling when the government (1-z) does not implement a reward and punishment mechanism;

[0118] Table 3 The three-party game profit matrix of recyclers actively recycling when the government (1-z) does not implement a reward and punishment mechanism

[0119]

[0120] 4) The three-party game profit matrix of recyclers’ passive recycling when the government (1-z) does not implement a reward and punishment mechanism.

[0121]

[0122] Specifically, the evolutionary equilibrium analysis of recyclers. For recyclers, assuming that the expected return of choosing an active recycling strategy is U1, the expected return of choosing a passive recycling strategy is U2, and the average expected return is U, the replication dynamic equation of the recycler's strategy selection is F(x), and the expression is as follows:

[0123]

[0124] U=xU1+(1-x)U2,

[0125] The replication dynamic equation for the recycler strategy selection is:

[0126]

[0127] The first-order derivative of x and the set G(y) are:

[0128]

[0129] According to the stability theorem of differential equations, the probability of a recycler actively recycling must be in a stable state if: F(x) = 0 and

[0130] because Therefore, G(y) is an increasing function with respect to y.

[0131] So when hour, All x are in an evolutionary stable state and no stable strategy can be determined; when y<y * hour, x = 0 is the evolutionary stable strategy of the recycler, which means that the probability of consumers actively participating in recycling is lower than When y>y, the recycler will choose the strategy of “passive recycling”; on the contrary, when y>y * When x=1, it is the evolutionary stable strategy of the recycler, that is, the probability of consumers actively participating in recycling is higher than When recycling, active recycling is the best strategy for third-party recyclers.

[0132] Specifically, for consumers, the evolutionary equilibrium analysis is as follows: for consumers, assuming that the expected return of choosing an active recycling strategy is S1, the expected return of choosing a passive participation strategy is S2, and the average expected return is S. The replication dynamic equation of consumer strategy selection is F(y), which is expressed as follows:

[0133] S1=xz[(R2-C2)q+ω2M+A-α2K2]+(1-x)z[(R2-C2)q+A-α2K2]+x(1-z)[(R2-C2)q+ω2M-α2K2]+(1-x)(1-z)[(R2-C2)q-α2K2]

[0134] =xω2M+zA+(R2-C2)q-α2K2

[0135] S2=xz[R2(q+λq)-C2q]+(1-x)z(R2-C2)q+x(1-z)[R2(q+λq)-C2q]+(1-x)(1-z)(R2-C2)q

[0136] =xR2λq+(R2-C2)q

[0137] S=yS1+(1-y)S2

[0138] The replication dynamic equation for consumer strategy selection is:

[0139]

[0140] The first-order derivative of y and the set G(z) are:

[0141]

[0142] G(z)=x(ω2M-R2λq)+zA-α2K2

[0143] According to the stability theorem of differential equations, the probability of consumers actively participating in a stable state must satisfy: F(y) = 0 and because Therefore, G(z) is an increasing function with respect to z.

[0144] when hour, All y are in an evolutionary stable state, and a stable strategy cannot be determined; when z < z * hour, y = 0 is the consumer's evolutionary stable strategy, indicating that the probability of the government implementing a reward and punishment mechanism is lower than When consumers choose to passively participate in recycling,

[0145] If z>z *, y = 1 is the consumer's evolutionary stable strategy, that is, the probability that the government implements a reward and punishment mechanism is higher than When recycling, actively participating in recycling is the best strategy for consumers.

[0146] Specifically, the evolutionary equilibrium analysis of government decision-making, for the government, assuming that the expected benefit of choosing to implement the reward and punishment mechanism strategy is W1, the expected benefit of choosing not to implement the reward and punishment mechanism is W2, the average expected benefit is W, and the replication dynamic equation of government strategy selection is F(z), which is expressed as follows:

[0147]

[0148] W2=xy(F2-N)+x(1-y)(-N)+(1-x)y(-N)+(1-x)(1-y)(-JN)

[0149] =xJ+yJ+xy(F2-J)-JN

[0150] W=zW1+(1-z)W2

[0151] The replication dynamic equation for government strategy selection is:

[0152]

[0153] The first-order derivative of z and the set G(x) are:

[0154]

[0155] According to the stability theorem of differential equations, the probability that the government chooses to implement the reward and punishment mechanism must be in a stable state if: F(z) = 0 and

[0156] because Therefore, G(x) is a decreasing function with respect to x.

[0157] when When G(x)=0, All z are in an evolutionary stable state, and no stable strategy can be determined;

[0158] When x<x * When G(x)>0, z = 0 is the government's evolutionary stable strategy, which means that the probability of recyclers actively recycling is lower than When the government chooses the strategy of “not implementing a reward and punishment mechanism”;

[0159] When x>x * When z = 1, it is the government's evolutionary stable strategy, that is, the probability that the recycler actively recycles is higher than When the government is faced with a problem, choosing to "implement a reward and punishment mechanism" is the best strategy for the government.

[0160] The three-way replication dynamic equation is as follows

[0161]

[0162] In addition, the stability analysis of the equilibrium point of the three-party evolutionary game is also included.

[0163] From F(x)=0,F(y)=0,F(z)=0, we can get the system equilibrium points: E1(0,0,0), E2(1,0,0), E3(1,1,0),

[0164] E4(1,0,1), E5(0,1,0), E6(0,1,1), E7(0,0,1), E8(1,1,1).

[0165] The Jacobian matrix of the three-party evolutionary game system is:

[0166]

[0167] Substitute the eight equilibrium points E1 to E8 into J 11 , J 22 , J 33 , we can get each equilibrium point

[0168]

[0169] F1+N>βS+A+C3, A+τQ+ω2M>G2+R2λq,

[0170] and When it is not less than 0 at the same time as A-G2, that is, when the sum of the reputational impacts on the local government regulatory department is greater than the sum of the cost it pays for active supervision and the subsidy value given, the sum of the cost of consumers' active participation in recycling and the benefits they get from free riding is less than the sum of the benefits they get from active participation in recycling and the reward value received from the local government regulatory department, the sum of the cost of recyclers' active recycling and the benefits they get from free riding is less than the sum of the benefits they get from active recycling and the rewards and punishments received from the local government regulatory department and the value of the decline in market share, and the input cost of recyclers' active recycling is greater than the value of the rewards and punishments received from the local government and the sum of the market share decline value, and the cost of consumers' active recycling is greater than the rewards received from the local government for their active participation in recycling. When these two things do not happen at the same time, E8(1,1,1) is an evolutionary stable point, corresponding to the strategy combination of active recycling, active participation in recycling, and active supervision. This is also the optimal equilibrium state that the participants of the express packaging recycling system under government regulation want to achieve. This paper conducts simulation analysis on this stable point.

[0171] In summary, the game analysis method of the enthusiasm of express packaging recycling entities under this reward and punishment mechanism, and the replication dynamic equation of recyclers are:

[0172]

[0173] The consumer's replication dynamics equation is:

[0174]

[0175] The government's replication dynamic equation:

[0176]

[0177] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0178] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism, characterized by: The steps include: Step 1: Model assumptions and parameter settings, and make the following assumptions: 1) The three parties involved in the game, recyclers, consumers and the government, are all bounded rational participants. Under bounded rationality conditions, each player often cannot find their own optimal strategy at the beginning, but adjusts their own strategy based on experience; 2) In the recycler-consumer-government evolutionary game model, the recycler's strategy choices include active recycling and passive recycling, the consumer's strategy choices include active participation and passive participation, and the government's strategy choices include implementing a reward and punishment mechanism and not implementing a reward and punishment mechanism. x, y, and z are used to represent the probability that the recycler actively recycles, the consumer actively participates in the recycling of express packaging, and the government implements an active regulatory strategy, and 0<x, y, z<1; 3) When only one party, recyclers or consumers, actively participates in the recycling of express packaging, the party that passively participates in the recycling can obtain additional benefits through "free-riding" behavior. Step 2: Construct the government-recycler-consumer three-party evolutionary game model and set up the corresponding matrix; Step 3: Replicate the dynamic equation and analyze the evolutionary equilibrium point, including the evolutionary equilibrium analysis of recyclers, consumers and government decision-making; Step 4: Based on the evolutionary game theory and Lyapunov system stability judgment method, conduct stability analysis of the equilibrium point of the three-party evolutionary game; Step 5: Through MATLAB numerical simulation analysis, we can obtain the influence of initial probability on the evolution path of the three-party game subject and the influence of different factors on the evolution path of the three-party game subject.

2. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The active recycling of the recyclers is reflected in the research and development of recycling technology, investment in and improvement of facilities and equipment, etc., and the active participation of the consumers is reflected in the correct classification, collection and transportation of waste to recycling companies.

3. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The implementation of the reward and punishment mechanism strategy mainly refers to the measures that government regulatory authorities can use the reward and punishment mechanism to reward and subsidize consumers and recyclers who actively participate in recycling, and punish recyclers who passively participate in express packaging recycling.

4. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: In the step 1, the benefits allocated to recyclers and consumers for actively participating in the recycling of express packaging should be greater than the benefits they obtain through "free riding", that is, it is assumed in this article that ω1M>R1λq,ω2M>R2λq.

5. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 2 is characterized by: The ω1M>R1λq,ω2M>R2λq, wherein: R1: The unit recycling income of the recycler for the express packaging; C1: The unit recycling cost of express packaging by recyclers, mainly including unit recycling price, human resource costs, facilities and equipment input costs; R2: Unit recycling revenue of consumers recycling express packaging; C2: The unit recycling cost of express packaging by consumers, mainly including the time cost invested, etc. q: The amount of recycled express packaging; α1: The degree of efforts made by recyclers to actively participate in recycling, mainly referring to the research and development of recycling technology, investment and improvement of facilities and equipment, etc., 0<α1<1; α2: The degree of effort of consumers to actively participate in recycling, mainly referring to the correct classification, collection, and transportation of waste to recycling companies, etc., 0<α2<1; K1: The recycler’s own capability level; K2: Consumers’ own ability level; M: Additional revenue created when both recyclers and consumers actively participate in recycling; ω1: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to recyclers, 0<ω1<1; ω2: the distribution rate of the additional revenue created when both recyclers and consumers actively participate in recycling to consumers, 0<ω2<1; λ: When only one party, the recycler or the consumer, actively participates in recycling, the unit profit increase rate that the party that passively participates in recycling can obtain additional benefits through "free riding" behavior; γb: The negative recycling behavior of recyclers leads to a decrease in market share expectations and consumer dissatisfaction γ (0<γ<1); βS: When the government implements the reward and punishment mechanism, it gives financial subsidies to recyclers with positive attitudes, and the subsidy intensity is β, 0<β<1; When the government implements a reward-penalty mechanism, the penalty imposed on recyclers who adopt a negative attitude is the intensity of supervision φ (0<φ<1); A: When the government implements a reward and punishment mechanism, it rewards consumers who actively participate in recycling; F1: The benefits gained from the improvement of the government’s image and social credibility when it implements a reward and punishment mechanism; F2: Recyclers and consumers actively participate in the express packaging recycling industry chain. The express packaging recycling and reuse industry is developing well, with obvious effects on environmental improvement. The government (local government) has received awards from higher-level governments. C3: administrative costs incurred when the government implements the reward and punishment mechanism; J: When the government does not implement a reward and punishment mechanism, and when recyclers and consumers adopt a passive strategy, the packaging recycling and reuse industry lags behind, leading to worsening environmental pollution and punishment from higher-level governments on the government (local government); N: When the government does not implement a reward and punishment mechanism, recyclers and consumers will lose their sense of dependence and trust in it, which will bring adverse effects to themselves.

6. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The matrix in step 2 includes: 1) The three-party game profit matrix of recyclers actively recycling under the government (z) implementation of the reward and punishment mechanism; 2) The three-party game profit matrix of recyclers’ passive recycling under the government (z) implementation of the reward and punishment mechanism; 3) The three-party game profit matrix of recyclers actively recycling when the government (1-z) does not implement a reward and punishment mechanism; 4) The three-party game profit matrix of recyclers’ passive recycling when the government (1-z) does not implement a reward and punishment mechanism.

7. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The evolutionary equilibrium analysis of the recycler, for the recycler, assume that the expected return of the active recycling strategy is U1, the expected return of the passive recycling strategy is U2, and the average expected return is U. The replication dynamic equation of the recycler's strategy selection is F(x), and the expression is as follows: U=xU1+(1-x)U2, The replication dynamic equation of the recycler strategy selection is:

8. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The evolutionary equilibrium analysis of the consumer, for consumers, assume that the expected return of choosing an active recycling strategy is S1, the expected return of choosing a passive participation strategy is S2, the average expected return is S, and the replication dynamic equation of consumer strategy selection is F(y), which is expressed as follows S1=xz[(R2-C2)q+ω2M+A-α2K2]+(1-x)z[(R2-C2)q+A-α2K2] +x(1-z)[(R2-C2)q+ω2M-α2K2]+(1-x)(1-z)[(R2-C2)q-α2K2] =xω2M+zA+(R2-C2)q-α2K2 S2=xz[R2(q+λq)-C2q]+(1-x)z(R2-C2)q+x(1-z)[R2(q+λq)-C2q] +(1-x)(1-z)(R2-C2)q =xR2λq+(R2-C2)q S=yS1+(1-y)S2 The replication dynamic equation for consumer strategy selection is:

9. The game analysis method for the enthusiasm of express packaging recycling entities under a reward and punishment mechanism according to claim 1 is characterized by: The evolutionary equilibrium analysis of government decision-making, for the government, assumes that the expected benefit of the strategy of implementing the reward and punishment mechanism is W1, the expected benefit of not implementing the reward and punishment mechanism is W2, the average expected benefit is W, and the replication dynamic equation of the government strategy selection is F(z), which is expressed as follows: W2=xy(F2-N)+x(1-y)(-N)+(1-x)y(-N)+(1-x)(1-y)(-JN) =xJ+yJ+xy(F2-J)-JN W=zW1+(1-z)W2 The replication dynamic equation for government strategy selection is:

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