Discreet investors exert greater influence on cooperation in the public goods game

This paper studies the evolutionary process of cooperative behavior in a public goods game model with heterogeneous investment strategies in square lattices.In the proposed model,players are divided into defectors,cooperators and discreet investors.Among these,defectors do not participate in investing,discreet investors make heterogeneous investments based on the investment behavior and cooperation value of their neighbors,and cooperators invest equally in each neighbor.In real life,heterogeneous investment is often accompanied by time or economic costs.The discreet investors in this paper pay a certain price to obtain their neighbors'investment behavior and cooperation value,which quantifies the time and economic costs of the heterogeneous investment process.The results of Monte Carlo simulation experiments in this study show that discreet investors can effectively resist the invasion of the defectors,form a stable cooperative group and expand the cooperative advantage in evolution.However,when discreet investors pay too high a price,they lose their strategic advantage.The results in this paper help us understand the role of heterogeneous investment in promoting and maintaining human social cooperation.

Strategy dominance mechanism of autonomous collaboration in unmanned swarm within the framework of public goods game

The key advantage of unmanned swarm operation is its autonomous cooperation. How to improve the proportion of cooperators is one of the key issues of autonomous collaboration in unmanned swarm operations. This work proposes a strategy dominance mechanism of autonomous collaboration in unmanned swarm within the framework of public goods game. It starts with the requirement analysis of autonomous collaboration in unmanned swarm;and an aspiration-driven multiplayer evolutionary game model is established based on the requirement. Then the average abundance function and strategy dominance condition of the model are constructed by theoretical derivation. Furthermore, the evolutionary mechanism of parameter adjustment in swarm cooperation is revealed via simulation,and the influences of the multiplication factor r, aspiration levelα, threshold m and other parameters on the strategy dominance conditions were simulated for both linear and threshold public goods games(PGGs) to determine the strategy dominance characteristics;Finally, deliberate proposals are suggested to provide a meaningful exploration in the actual control of unmanned swarm cooperation.

Maintenance of cooperation induced by punishment in public goods games

In this paper, we study the public goods games with punishment by adopting the well-known approximate best response dynamics. It shows that the evolution of cooperation is affected by two aspects when other parameters are fixed. One is the punishment mechanism which can avoid the dilemma of lacking investment, and the other is the degree of rationality. Theoretical analysis and numerical results indicate that the existence of punishment mechanism and distribution of rationality are the keys to the enhancement of cooperation level. We also testify that they can heavily influence the payoffs of system as well. The findings in this paper may provide a deeper understanding of some social dilemmas.

Stochastic evolutionary public goods game with first and second order costly punishments in finite populations

We study the stochastic evolutionary public goods game with punishment in a finite size population. Two kinds of costly punishments are considered, i.e., first-order punishment in which only the defectors are punished, and second-order punishment in which both the defectors and the cooperators who do not punish the defective behaviors are punished. We focus on the stochastic stable equilibrium of the system. In the population, the evolutionary process of strategies is described as a finite state Markov process. The evolutionary equilibrium of the system and its stochastic stability are analyzed by the limit distribution of the Markov process. By numerical experiments, our findings are as follows.（i） The first-order costly punishment can change the evolutionary dynamics and equilibrium of the public goods game, and it can promote cooperation only when both the intensity of punishment and the return on investment parameters are large enough.（ii）Under the first-order punishment, the further imposition of the second-order punishment cannot change the evolutionary dynamics of the system dramatically, but can only change the probability of the system to select the equilibrium points in the ＂C＋P＂ states, which refer to the co-existence states of cooperation and punishment. The second-order punishment has limited roles in promoting cooperation, except for some critical combinations of parameters.（iii） When the system chooses＂C＋P＂ states with probability one, the increase of the punishment probability under second-order punishment will further increase the proportion of the ＂P＂ strategy in the ＂C＋P＂ states.

Punishment in optional public goods games

In this work, the optional public goods games with punishment are studied. By adopting the approximate best response dynamics, a micro model is given to explain the evolutionary process. Simultaneously, the magnitude of rationality is also considered. Under the condition of bounded rationality which provides a light to interpret phenomena in human society, the model leads to two types of equilibriums. One is the equilibrium without punishers and the other is the equilibrium including only punishers and cooperators. In addition, the effects of rationality on equilibriums are briefly investigated.

Evolution of Cooperation in Public Goods Games

We investigate the evolution of cooperation with evolutionary public goods games based on finite populations, where four pure strategies： cooperators, defectors, punishers and loners who are unwilling to participate are considered. By adopting approximate best response dynamics, we show that the magnitude of rationality not only quantitatively explains the experiment results in [Nature （London） 425 （2003） 390], but also it will heavily influence the evolution of cooperation. Compared with previous results of infinite populations, which result in two equilibriums, we show that there merely exists a special equilibrium cooperation. In addition, we characterize that loner＇s and the relevant high value of bounded rationality will sustain payoff plays an active role in the maintenance of cooperation, which will only be warranted for the low and moderate values of loner＇s payoff. It thus indicates the effects of rationality and loner＇s payoff will influence the cooperation. Finally, we highlight the important result that the introduction of voluntary participation and punishment will facilitate cooperation greatly.

Fitness of others'evaluation effect promotes cooperation in spatial public goods game

Payoff-driven strategy updating rule has always been adopted as a classic mechanism,but up to now,there have been a great many of researches on considering other forms of strategy updating rules,among which pursuing high fitness is one of the most direct and conventional motivations in the decision-making using game theory.But there are few or no researches on fitness from the perspective of others'evaluation.In view of this,we propose a new model in which the evaluation effect with fitness-driven strategy updating rule is taken into consideration,and introduce an evaluation coefficient to present the degree of others'evaluation on individual's behavior.The cooperative individuals can get positive evaluation,otherwise defective individuals get negative evaluation,and the degree of evaluation is related to the number of neighbors who have the same strategy of individual.Through numerical simulation,we find that the evaluation effect of others can enhance the network reciprocity,thus promoting the cooperation.For a strong dilemma,the higher evaluation coefficient can greatly weaken the cooperation dilemma;for a weak one,the higher evaluation coefficient can make cooperator clusters spread faster,however,there is no significant difference in the level of cooperation in the final stable state among different evaluation coefficients.The cooperation becomes more flourish as the number of fitness-driven individuals increases,when all individuals adopt fitness-driven strategy updating rule,the cooperators can quickly occupy the whole population.Besides,we demonstrate the robustness of the results on the WS small-world network,ER random network,and BA scalefree network.

EVOLUTIONARY PUBLIC GOODS GAMES BASED ON HISTORICAL PAYOFFS

We investigate the evolution of cooperation in public goods game based on individuals' historical payoffs. In particular, the fitness of individuals are characterized by two types of payoffs, which are obtained by acting as cooperators and defectors, respectively. Both of payoffs are the linear combination of the current payoffs and the cumulative historical payoffs. The results show that cooperation is enhanced by an increasing memory effect with a wide range of related factors. To explain this phenomenon, we plot some representative snapshots of the population and scrutinize the mean fitness of cooperators and defectors along the boundary. It is found that increasing memory effect induces a positive feedback mechanism for cooperators to expand their districts. Defectors can just survive through forming narrower clusters to exploit cooperators more widely. The threshold values for cooperators and defectors vanishing under the influence of noise are also investigated.

Emergence of Group Cooperation in Public Goods Game on Regular Small-World Network

The regular small-world network, which contains the properties of small-world network and regular network, has recently received substantial attention and has been applied in researches on 2-person games. However, it is a common phenomenon that cooperation always appears as a group behavior. In order to investigate the mechanism of group cooperation, we propose an evolutionary multi-person game model on a regular small-world network based on public goods game theory. Then, to make a comparison of frequency of cooperation among different networks, we carry out simulations on three kinds of networks with the same configuration of average degree： the square lattice, regular small-world network and random regular network. The results of simulation show that the group cooperation will emerge among these three networks when the enhancement factor r exceeds a threshold. Furthermore, time required for full cooperation on regular small-world network is slightly longer than the other networks, which indicates that the compact interactions and random interactions will promote cooperation, while the longer-range links are the obstacles in the emergence of cooperation. In addition, the cooperation would be promoted further by enhancing the random interactions on regular small-world network.

Evolution of donations on scale-free networks during a COVID-19 breakout

Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners’ dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries,legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors,illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found.At the same time, it is discovered that the initial states of the population have a great impact on the steady states;thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.