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1.
Heterogeneous aspirations promote cooperation in the prisoner's dilemma game
Matjaž Perc, Zhen Wang, 2010, original scientific article

Abstract: To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hopeof successful reproduction. In structured populations the array of those that are eligible to act as strategy sources is bounded to the immediate neighbors of each individual. But which one of these strategy sources should potentially be copied? Previous research dealt with this question either by selecting the fittest or by selecting one player uniformly at random. Here we introduce a parameter that interpolates between these two extreme options. Setting equal to zero returns the random selection of the opponent, while positive favor the fitter players. In addition, we divide the population intotwo groups. Players from group select their opponents as dictated by the parameter , while players from group do so randomly irrespective of . We denote the fraction of players contained in groups and by and , respectively. The two parameters and allow us to analyze in detail how aspirations in the context of the prisoner's dilemma game influence the evolution of cooperation. We find that for sufficiently positive values of there exist a robust intermediate for which cooperation thrives best. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. We also provide complete phase diagrams depicting the dependence of the impact of and for different values of , and contrast the validity of ourconclusions by means of an alternative model where individual aspiration levels are subject to evolution as well. Our study indicates that heterogeneity in aspirations may be key for the sustainability of cooperation in structured populations.
Keywords: evolutionary game theory, prisoner's dilemma, spatial games, aspirations, social systems, physics and society
Published: 19.06.2017; Views: 609; Downloads: 230
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2.
Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game
Matjaž Perc, 2007, original scientific article

Abstract: We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner's dilemma game. We find that Gaussian-distributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed.
Keywords: stochastic systems, spatial resonance, stochastic payoff variations, nonlinear systems, noise, spatial dynamics, mathematical models, prisoner's dilemma
Published: 07.06.2012; Views: 1277; Downloads: 67
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3.
Double resonance in cooperation induced by noise and network variation for an evolutionary prisoner's dilemma
Matjaž Perc, 2006, original scientific article

Abstract: We study effects of slowly varying small-world topology and additive spatiotemporal random variations, introduced to the payoffs of a spatial prisoner's dilemma game, on the evolution of cooperation. We show that there exists an optimal fraction of shortcut links, constituting the variable complex network of participating players of the game, for which noise-induced cooperation is resonantly enhanced, thus marking a double resonance phenomenon in the studied system. The double resonance is attributed to the time-dependence of the connectivity structure that induces a tendency towards the mean-field behaviour in the limit of random graphs. We argue that random payoff disturbances and complex network topology are two potent extrinsic factors able to boost cooperation, thus representing a viable escape hatch out of evolutionary stalemate.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, prisoner's dilemma
Published: 07.06.2012; Views: 1041; Downloads: 263
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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: 366; Downloads: 243
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7.
Resolution of the stochastic strategy spatial prisoner's dilemma by means of particle swarm optimization
Jianlei Zhang, Chunyan Zhang, Tianguang Chu, Matjaž Perc, 2011, original scientific article

Abstract: We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.
Keywords: cooperation, prisoner's dilemma, particle swarm optimization, stochastic strategies
Published: 19.06.2017; Views: 501; Downloads: 250
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8.
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: 502; Downloads: 241
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9.
Coevolution of teaching activity promotes cooperation
Attila Szolnoki, Matjaž Perc, 2008, original scientific article

Abstract: Evolutionary games are studied where the teaching activity of players can evolve in time. Initially all players following either the cooperative or defecting strategy are distributed on a square lattice. The rate of strategy adoption is determined by the payoff difference and a teaching activity characterizing the donor's capability to enforce its strategy on the opponent. Each successful strategy adoption process is accompanied by an increase in the donor's teaching activity. By applying an optimum value of the increment, this simple mechanism spontaneously creates relevant inhomogeneities in the teaching activities that support the maintenance of cooperation for both the prisoner's dilemma and the snowdrift game.
Keywords: evolutionary game theory, prisoner's dilemma, spatial games, snowdrift game, coevolution
Published: 30.06.2017; Views: 432; Downloads: 264
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10.
Emergence of multilevel selection in the prisoner's dilemma game on coevolving random networks
Attila Szolnoki, Matjaž Perc, 2009, original scientific article

Abstract: We study the evolution of cooperation in the prisoner's dilemma game, whereby a coevolutionary rule is introduced that molds the random topology of the interaction network in two ways. First, existing links are deleted whenever a player adopts a new strategy or its degree exceeds a threshold value; second, new links are added randomly after a given number of game iterations. These coevolutionary processes correspond to the generic formation of new links and deletion of existing links that, especially in human societies, appear frequently as a consequence of ongoing socialization, change of lifestyle or death. Due to the counteraction of deletions and additions of links the initial heterogeneity of the interaction network is qualitatively preserved, and thus cannot be held responsible for the observed promotion of cooperation. Indeed, the coevolutionary rule evokes the spontaneous emergence of a powerful multilevel selection mechanism, which despite the sustained random topology of the evolving network, maintains cooperation across the whole span of defection temptation values.
Keywords: evolutionary game theory, prisoner's dilemma, spatial games, coevolution, social systems
Published: 30.06.2017; Views: 702; Downloads: 263
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