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Adaptive and bounded investment returns promote cooperation in spatial public goods games
Xiaojie Chen, Yongkui Liu, Yonghui Zhou, Long Wang, Matjaž Perc, 2012, original scientific article

Abstract: The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.
Keywords: cooperation, public goods, social dilemmas, physics of social systems
Published: 19.06.2017; Views: 287; Downloads: 192
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Different reactions to adverse neighborhoods in games of cooperation
Chunyan Zhang, Jianlei Zhang, Franz Weissing, Matjaž Perc, Guangming Xie, Long Wang, 2012, original scientific article

Abstract: In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.
Keywords: cooperation, public goods, phase transitions, social dilemmas, coevolution, physics of social systems
Published: 19.06.2017; Views: 451; Downloads: 198
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Evolution of interactions and cooperation in the spatial prisoner's dilemma game
Chunyan Zhang, Jianlei Zhang, Guangming Xie, Long Wang, Matjaž Perc, 2011, original scientific article

Abstract: We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.
Keywords: evolutionary games, prisoner's dilemma, coevolution, complex networks, friendship
Published: 19.06.2017; Views: 237; Downloads: 191
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Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game
Yongkui Liu, Xiaojie Chen, Lin Zhang, Long Wang, Matjaž Perc, 2012, original scientific article

Abstract: Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed winstay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related winstay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.
Keywords: social dilemmas, prisoner's dilemma, cooperation, networks
Published: 19.06.2017; Views: 358; Downloads: 196
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Beyond pairwise strategy updating in the prisoner's dilemma game
Xiaofeng Wang, Matjaž Perc, Yongkui Liu, Xiaojie Chen, Long Wang, 2012, original scientific article

Abstract: In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.
Keywords: cooperation, social dilemma, wisdom of crowds, phase transitions, physics of social systems
Published: 23.06.2017; Views: 235; Downloads: 181
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Limit cycle bifurcated from a center in a three dimensional system
Bo Sang, Brigita Ferčec, Qin-Long Wang, 2016, original scientific article

Abstract: Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $Є^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.
Keywords: algorithms, three dimensional systems, focal value, limit cycle, Hopf bifurcation, center
Published: 08.08.2017; Views: 884; Downloads: 78
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