Positive excitation noise modeling method for network game

Abstract

The invention discloses a positive excitation noise modeling method for network gaming, which relates to the technical field of man-machine gaming, and comprises the steps of S1, gaming model construction, S2, strategy representation and income calculation, S3, strategy updating mechanism, S4, state transition and stability analysis, and S5, network structure. The invention provides a modeling method for maintaining and promoting cooperation by introducing positive excitation noise in a network game, by introducing a medium-level mutation rate, the cooperation level can be improved under the condition that the ratio of income to cost is only slightly higher than 1, and the problem that cooperation is difficult to maintain in a traditional game model is solved; the method is also suitable for a game scene in a network structure, especially in a simple lattice network, the mutation rate of a medium degree can effectively stimulate cooperation behaviors between individuals, and the practicability and wide applicability of the model are enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of human-computer gaming, and particularly relates to a positive incentive noise modeling method for network gaming. Background Art

[0002] In evolutionary game theory, the maintenance and evolution of cooperation have always been one of the core research issues. In the real world, cooperation among individuals widely exists in biological, social, and economic systems. However, the maintenance of cooperation faces the threat of "free riders", that is, those individuals who benefit from cooperation but do not pay costs. Therefore, exploring the mechanism by which cooperation can be maintained has important theoretical significance and practical value.

[0003] Game theory provides a micro-theoretical tool for studying cooperation phenomena. Among them, direct reciprocity is an important cooperation evolution mechanism. However, it requires the benefit-cost ratio to exceed a certain threshold to achieve high-level cooperation. When the benefit-cost ratio is between 1 and 2, cooperation is difficult to maintain. To address the above problems, the following solutions are proposed. Summary of the Invention

[0004] The purpose of the present invention is to provide a positive incentive noise modeling method for network gaming, which can maintain and promote cooperation by introducing positive incentive noise. By introducing a medium-level mutation rate, high-level cooperation can be achieved even when the benefit-cost ratio is only slightly higher than 1, solving the problem that cooperation is difficult to maintain when the benefit-cost ratio is between 1 and 2 in the prior art.

[0005] To solve the above technical problems, the present invention is realized through the following technical solutions:

[0006] The present invention is a positive incentive noise modeling method for network gaming, including:

[0007] Step S1, game model construction: The donation game model and its extended form, the repeated donation game, are adopted. In the donation game, the player faces two choices: cooperation and betrayal. When cooperating, the donor pays a cost c, and the recipient obtains a benefit b; when betraying, there is no cost or benefit, and its payoff matrix clarifies the payoff situation under different strategy combinations. The repeated donation game simulates multiple interactions among participants, and the participants make decisions according to the Memory-1 strategy, that is, make this round of choices based on the actions of themselves and their opponents in the previous round;

[0008] Step S2, strategy representation and payoff calculation: Set a strategy array for each participant and calculate the average payoff of the individual;

[0009] Step S3, strategy update mechanism: Use the pairwise comparison process to update the strategy, mutate with probability u, and imitate with probability 1 - u;

[0010] Step S4, State Transition and Stability Analysis: Describe the change of cooperation probability using the state transition matrix, and obtain the cooperation probability and payoff in the stable state;

[0011] Step S5, Network Structure: In a simple lattice network, each node in the lattice network is a participant, and the edges in the lattice network are the connections generated between the participant and its neighbors. Each participant only plays the game with its connected neighbors;

[0012] In the step S3, the pairwise comparison process is used in the strategy update mechanism to achieve individual strategy update, including two ways, namely mutation with probability u and imitation with probability 1 - u;

[0013] When imitating, the focal individual randomly selects a role model R from its neighbors, and the imitation probability is:

[0014]

[0015] where β is the selection intensity, π F is the payoff of the focal individual F, and π R is the payoff of the randomly selected role model R.

[0016] Furthermore, in the donation game of the step S1, Game Model Construction, the player faces two choices: cooperation and betrayal;

[0017] When cooperating, the donor pays a cost c and the recipient obtains a benefit b; when betraying, there is no cost or benefit. The repeated donation game simulates multiple interactions of the participants, and the participants make decisions according to the Memory-1 strategy and make choices in this round based on the actions of themselves and their opponents in the previous round.

[0018] Furthermore, in the step S2, Strategy Representation and Payoff Calculation, the strategy array is set as:

[0019] p = [P CC , P CD , P DC , P DD ;

[0020] where P CC is the probability of cooperation in this round when both parties cooperated in the previous round, P CD is the probability of cooperation in this round when the individual cooperated and the opponent betrayed in the previous round, P DC is the probability of cooperation in this round when the individual betrayed and the opponent cooperated in the previous round, and P DD is the probability of cooperation in this round when both parties betrayed in the previous round.

[0021] Furthermore, in the step S2, Strategy Representation and Payoff Calculation, the formula for calculating the individual payoff is:

[0022] πi = ∑j ≠iπ(Si, Sj) / (n);

[0023] In the formula, π i is the average payoff of individual i; π(S i , S j ) is the payoff obtained by individual i when individual i adopts strategy S i and individual j adopts strategy S j in the game; n is the degree of the node where individual i is located.

[0024] Furthermore, in the state transition and stability analysis in step S4, the state transition matrix is:

[0025]

[0026] In the formula, p CC q CC means that in the previous round of the game, both sides chose to cooperate, and in this round of the game, both sides still choose to cooperate; p CC (1 - q CC ) means that the central player chooses to cooperate while the opponent player chooses to defect; (1 - p CC )q CC means that the central player chooses to defect while the opponent player chooses to cooperate; (1 - p CC )(1 - q CC ) means that both players choose to defect; p CD q DC means the probability that in this round of the game, both players choose to cooperate when the central player chose to cooperate and its opponent chose to defect in the previous round of the game; p CD (1 - q DC ) means the probability that in this round of the game, the central player chooses to cooperate and the opponent player chooses to defect when the central player chose to cooperate and its opponent chose to defect in the previous round of the game; and so on. The third row in the matrix represents the situation where the central player chose to defect and the opponent player chose to cooperate in the previous round of the game, and the fourth row represents the situation where both the central player and the opponent player chose to defect in the previous round of the game.

[0027] The present invention has the following beneficial effects:

[0028] The present invention provides a modeling method for maintaining and promoting cooperation in network games by introducing positive incentive noise. By introducing a medium-level mutation rate, it can improve the cooperation level when the payoff-cost ratio is only slightly higher than 1, and solves the problem that cooperation is difficult to maintain in traditional game models; this method is also applicable to game scenarios in network structures. Especially in a simple lattice network, a medium mutation rate can effectively stimulate the cooperative behavior between individuals, enhancing the practicality and wide applicability of the model.

[0029] Of course, it is not necessary for any product implementing the present invention to achieve all the above-mentioned advantages simultaneously. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0031] Figure 1 is a schematic flow chart of the present invention;

[0032] Figure 2 is the income matrix of the donation game of the present invention;

[0033] Figure 3 is a schematic diagram showing the influence of mutation rate on cooperation rate under the simple lattice network of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0035] Please refer to Figure 1 as shown, the present invention is a positive incentive noise modeling method for network games, including:

[0036] Step S1, game model construction: The donation game model and its extended form, the repeated donation game, are adopted. In the donation game, the player faces two choices: cooperation and betrayal. When cooperating, the donor pays a cost c, and the recipient obtains a benefit b; when betraying, there is no cost or benefit. Its income matrix clarifies the benefits in different strategy combinations. The repeated donation game simulates the multiple interactions of the participants. The participants make decisions according to the Memory-1 strategy, that is, make this round of choices based on the actions of themselves and their opponents in the previous round;

[0037] Step S2, strategy representation and benefit calculation: Set a strategy array for each participant and calculate the average benefit of the individual;

[0038] Step S3, strategy update mechanism: Use the pairwise comparison process to update the strategy, mutate with probability u, and imitate with probability 1 - u;

[0039] Step S4, State Transition and Stability Analysis: Describe the change in cooperation probability using the state transition matrix, and find the cooperation probability and payoff in the stable state;

[0040] Step S5, Network Structure: In a simple lattice network, each node in the lattice network is a participant, and the edges in the lattice network are the connections generated between participants and their neighbors. Each participant only plays the game with the neighbors it is connected to;

[0041] In the strategy update mechanism, the pairwise comparison process is used to update the individual strategy, including two methods, namely, mutating with probability u and imitating with probability 1 - u;

[0042] When imitating, the focal individual randomly selects a role model R from its neighbors, and the imitation probability is:

[0043]

[0044] where β is the selection intensity, π F is the payoff of the focal individual F, and π R is the payoff of the randomly selected role model R;

[0045] In the donation game for constructing the game model in Step S1, the player faces two choices: cooperation and betrayal;

[0046] When cooperating, the donor pays a cost c, and the recipient obtains a benefit b; when betraying, there is no cost or benefit. The repeated donation game simulates multiple interactions among participants. The participants make decisions based on the Memory-1 strategy and make choices in this round according to their own and their opponents' actions in the previous round;

[0047] In Step S2, Strategy Representation and Payoff Calculation, the strategy array is set as:

[0048] p = [P CC , P CD , P DC , P DD ;

[0049] where P CC is the probability of cooperation in this round when both parties cooperated in the previous round, P CD is the probability of cooperation in this round when the individual cooperated and the opponent betrayed in the previous round, P DC is the probability of cooperation in this round when the individual betrayed and the opponent cooperated in the previous round, and P DD is the probability of cooperation in this round when both parties betrayed in the previous round;

[0050] In Step S2, Strategy Representation and Payoff Calculation, the formula for calculating the individual payoff is:

[0051] πi = ∑j ≠ iπ(Si, Sj) / (n);

[0052] In the formula, π i is the average return of individual i; π(S i , S j ) is the return obtained by individual i when individual i adopts strategy S i and individual j adopts strategy S j to play the game; n is the degree of the node where individual i is located;

[0053] In step S4, the state transition matrix in state transition and stability analysis is:

[0054]

[0055] In the formula, p CC q CC means that in the previous round of the game, both sides chose cooperation, and in this round of the game, both sides still choose cooperation; p CC (1 - q CC ) means that the central player chooses cooperation while the opponent player chooses betrayal; (1 - p CC )q CC means that the central player chooses betrayal while the opponent player chooses cooperation; (1 - p CC )(1 - q CC ) means that both player sides choose betrayal; p CD q DC means that in the previous round of the game, when the central player chose cooperation and its opponent chose betrayal, the probability that both players choose cooperation in this round; p CD (1 - q DC ) means that in the previous round of the game, when the central player chose cooperation and its opponent chose betrayal, the probability that the central player chooses cooperation and the opponent player chooses betrayal in this round; and so on. The third row in the matrix represents the situation where the central player chose betrayal and the opponent player chose cooperation in the previous round of the game, and the fourth row represents the situation where both the central player and the opponent player chose betrayal in the previous round of the game;

[0056] A specific application of this embodiment is:

[0057] The present invention uses the donation game model; the donation game is a game theory model used to study whether individuals are willing to sacrifice their own resources to help others without direct return; in the game, the donor can choose to donate part of the resources to the recipient, the recipient benefits, and the donor's own resources decrease; it reveals the driving force of altruistic behavior, such as reputation improvement, psychological satisfaction or long-term reciprocity, and also faces the free-rider problem; the donation game is widely used to analyze decision-making and cooperation mechanisms in situations such as charitable donations and social mutual assistance; in the donation game, players choose between cooperation and betrayal; cooperation brings a cost c and a benefit b to the cooperating players; defection incurs no cost and provides no benefit; the payoff matrix of the donation game is as Figure 2 shown;

[0058] The Repeated Donation Game is an extended form of the donation game, which simulates the dynamic changes of donation behavior among participants in multiple interactions; by studying the long-term strategy choices of individuals, it can reveal how cooperation, trust and altruistic behavior are formed and maintained in a group; in the repeated donation game, each participant can choose whether to donate in each round of the game, and the game is not played once, but repeated multiple rounds, and the results of each round may affect the decisions in subsequent rounds; participants may adopt different strategies, the ALLC strategy is to always donate and always choose cooperation; the opposite is the ALLD strategy, which always chooses to betray, that is, always chooses not to cooperate; the Tit-for-Tat strategy is the tit-for-tat strategy, and the participants who choose this strategy will copy the behavior of the other party in the previous round;

[0059] Consider a population of size N; individuals participate in a repeated donation game; assume that individuals make decisions on whether to cooperate based on the Memory-1 strategy, that is, the action of each participant in this round only considers the actions of himself and his opponent in the previous round; in a typical two-player game, there are four possible outcomes in each round of the game: CC: both cooperate; CD: oneself cooperates and the opponent betrays; DC: oneself betrays and the opponent cooperates; DD: both betray; the strategy of each participant can be described by an array: p = [PCC, PCD, PDC, PDD]; PCC represents the probability of choosing to cooperate in this round when both oneself and the opponent chose to cooperate in the previous round; PCD represents the probability of choosing to cooperate in this round when oneself chose to cooperate and the opponent chose to betray in the previous round; PDC represents the probability of choosing to cooperate in this round when oneself chose to betray and the opponent chose to cooperate in the previous round; PDD represents the probability of choosing to cooperate in this round when both oneself and the opponent chose to cooperate in the previous round; if all cooperation probabilities are 0 or 1, this strategy is called a deterministic strategy; if at least one probability is between the two, it is called a stochastic strategy; Memory-1 strategies include: always betray ALLD = (0, 0, 0, 0), always cooperate ALLC = (1, 1, 1, 1), tit-for-tat TFT = (1, 1, 0, 0)t, generous tit-for-tat GTFT = (1, 1, q, q), where q ∈ [0, 1] is the probability of forgiveness or the degree of generosity;

[0060] At any point in time, the composition of the population can be described by the strategies adopted; each individual i obtains an average payoff from all pairwise interactions:

[0061] πi = ∑j ≠ iπ(Si, Sj) / (n);

[0062] where π i is the average payoff of individual i; π(S i , S j ) is the payoff obtained by individual i when individual i adopts strategy S i and individual j adopts strategy S j in the game; n is the degree of the node where individual i is located;

[0063] Over time, individuals learn to adopt more profitable strategies; here, a pairwise comparison process is used, which is a variant of random imitation; when the focal individuals F modify their strategies, they can do so in two ways; with probability u, the focal individuals randomly adopt a new strategy representing mutation; with probability 1 - u, the focal individuals consider imitating the strategy of another member of the population, which corresponds to reproduction and selection; for this purpose, the focal participant randomly selects a role model R from the neighbors with probability p = 1 - u, and imitates the strategy of that neighbor with probability Pswitch and retains the original strategy with probability 1 - Pswitch without making changes; the formula for Pswitch is as follows:

[0064]

[0065] where β is the selection intensity, π F is the payoff of the focal individual F, and π R is the payoff of the randomly selected role model R;

[0066] The parameter β ≥ 0 represents the selection intensity, which reflects how clearly the payoffs are evaluated; the modeling of the imitation probability Pswitch takes into account the payoff gap between the two players and the selection intensity. When β = 0, the probability of changing the strategy is always 1 / 2, which means that the payoff gap becomes irrelevant; when β → ∞, the player will only adopt the other player's strategy when the other's payoff is higher, and the selection becomes very strong; for most simulations, β = 10 is chosen, which represents a medium-strength selection;

[0067] In the invention, the Memory-1 strategy set is adopted, that is, the action of each participant in this round only considers the actions of oneself and the opponent in the previous round; the strategy of each participant can be described using an array: p = [P CC , P CD , P DC , P DD ; where P CC is the probability of cooperation in this round when both parties cooperated in the previous round, P CD is the probability of cooperation in this round when oneself cooperated and the opponent defected in the previous round, P DC is the probability of cooperation in this round when oneself defected and the opponent cooperated in the previous round, P DD is the probability of cooperation in this round when both parties defected in the previous round; after one round of the game, the probability of cooperation of the participants will change, and the state transition matrix is as follows:

[0068]

[0069] where p CC q CCIn the previous round of the game, both sides chose cooperation, and in this round of the game, both sides still choose cooperation; p CC (1 - q CC ) means that the central player chooses cooperation while the opponent player chooses betrayal; (1 - p CC )q CC means that the central player chooses betrayal while the opponent player chooses cooperation; (1 - p CC )(1 - q CC ) means that both players choose betrayal; p CD q DC means that in the previous round of the game, when the central player chose cooperation and its opponent chose betrayal, the probability that both players choose cooperation in this round; p CD (1 - q DC ) means that in the previous round of the game, when the central player chose cooperation and its opponent chose betrayal, the probability that the central player chooses cooperation and the opponent player chooses betrayal in this round; and so on. The third row in the matrix represents the situation where the central player chose betrayal and the opponent player chose cooperation in the previous round of the game, and the fourth row represents the situation where both the central player and the opponent player chose betrayal in the previous round of the game;

[0070] After repeated games, the probability of cooperation among participants reaches a stable state, pMS = p. From this, the cooperation probability and payoff of participants at the stable state can be deduced using the evolutionary stable strategy; when the strategy is stable, the calculation process is as follows:

[0071] vM = v

[0072] v(M - E) = 0

[0073] p = (pCC, pCD, pDC, pDD)

[0074] q = (qCC, qCD, qDC, qDD)

[0075] v = (vCC, vCD, vDC, vDD)

[0076] = (v1, v2, v3, v4)

[0077] coop1 = vCC + vCD = v1 + v2

[0078] coop2 = vCC + vDC = v1 + v3

[0079] π1 = coop2 * b - coop1 * c

[0080] π2 = coop1 * b - coop2 * c

[0081] π1 is the payoff of the focal player, and coop1 is the cooperation rate of the focal player; when the concept of network is not introduced, the participants are default to be in a fully connected state, that is, if there are N participants, then each participant will play the repeated donation game with the other N - 1 participants; in the simple lattice network, each node in the lattice network is each participant, and the edges in the lattice network are the connections generated between the participants and their neighbors. Each participant only plays the game with the neighbors it is connected to, that is, each participant only plays the game with four neighbors to generate payoffs, ensuring the normal progress of the repeated donation game;

[0082] In Figure 3 it shows how the average cooperation rate C depends on the payoff-cost ratio b / c under the simple lattice network; in the limit of rare mutations u→0, this process is relatively clear; in this case, as the payoff-cost ratio increases, the increase in the cooperation rate is very slow; however, when mutations are introduced, it is found that the cooperation rate increases significantly; for the simple lattice network with population size N = 100, it is found that a slightly higher mutation rate (u = 0.03 to u = 0.05) is suitable for the Memory-1 strategy; the optimal mutation rate depends on the specific value of b / c; in network games, moderate noise increases the average cooperation rate.

[0083] In the description of this specification, the descriptions referring to terms such as "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0084] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not elaborate all the details, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A positive incentive noise modeling method for network games, characterized in that, It includes the following steps: Step S1, game model construction: The donation game and repeated donation game are adopted, and the participants make decisions according to the Memory-1 strategy; Step S2, strategy representation and payoff calculation: Set a strategy array for each participant and calculate the individual payoff; Step S3, strategy update mechanism: Use the pairwise comparison process to update the strategy, mutate with probability u, and imitate with probability 1 - u; Step S4, state transition and stability analysis: Use the state transition matrix to describe the change of cooperation probability, and find the cooperation probability and payoff in the stable state; Step S5, network structure: In a simple lattice network, each node in the lattice network is a participant, and the edges in the lattice network are the connections generated between the participants and their neighbors. Each participant only plays the game with the neighbors with connections; In the step S3, strategy update mechanism, the pairwise comparison process is used to realize the individual strategy update, including two methods, namely mutating with probability u and imitating with probability 1 - u; When imitating, the focal individual randomly selects a role model R from the neighbors, and the imitation probability is: where β is the selection intensity, π F is the payoff of the focal individual F, and π R is the payoff of the randomly selected role model R.

2. The positive incentive noise modeling method for network games according to claim 1, characterized in that In the donation game of the step S1, game model construction, the player faces two choices: cooperation and betrayal; When cooperating, the donor pays a cost c, and the recipient obtains a benefit b; there is no cost or benefit for betrayal. The repeated donation game simulates the multiple interactions of the participants. The participants make decisions according to the Memory-1 strategy and make this round of choices based on the actions of themselves and their opponents in the previous round.

3. A positive incentive noise modeling method for network games according to claim 1, characterized in that In the step S2, strategy representation and payoff calculation, the set strategy array is: p = [P CC , P CD , P DC , P DD ; Where P CC is the probability of cooperation in this round when both parties cooperated in the previous round, P CD is the probability of cooperation in this round when one cooperated and the other betrayed in the previous round, P DC is the probability of cooperation in this round when one betrayed and the other cooperated in the previous round, P DD is the probability of cooperation in this round when both parties betrayed in the previous round.

4. A positive incentive noise modeling method for network games according to claim 1, characterized in that, In the step S2, strategy representation and payoff calculation, the formula for calculating the individual payoff is: πi = ∑j ≠ iπ(Si, Sj) / (n); where, π i is the average payoff of individual i; π(S i , S j ) is the payoff obtained by individual i when individual i adopts strategy S i and individual j adopts strategy S j to play a game; n is the degree of the node where individual i is located.

5. A positive incentive noise modeling method for network games according to claim 1, characterized in that In the step S4, state transition and stability analysis, the state transition matrix is: where p CC q CC means that in the previous round of the game, both sides chose cooperation, and in this round of the game, both sides still choose cooperation; p CC (1 - q CC ) means that the central player chooses cooperation while the opponent player chooses betrayal; (1 - p CC )q CC means that the central player chooses betrayal while the opponent player chooses cooperation; (1 - p CC )(1 - q CC ) means that both players choose betrayal; p CD q DC means that in the case where the central player chose cooperation and its opponent chose betrayal in the previous round of the game, the probability that both players choose cooperation in this round; p CD (1 - q DC ) means that in the case where the central player chose cooperation and its opponent chose betrayal in the previous round of the game, the probability that the central player chooses cooperation and the opponent player chooses betrayal in this round; and so on. The third row in the matrix represents the case where the central player chose betrayal and the opponent player chose cooperation in the previous round of the game, and the fourth row represents the case where both the central player and the opponent player chose betrayal in the previous round of the game.

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