10,700 research outputs found

    On the Imitation Strategy for Games on Graphs

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    In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying the games on graphs. In this setting, players occupy the vertices of a graph and play the game only with their immediate neighbours. Various evolutionary dynamics have been studied in this setting for different games. Due to the complexity of the analysis, however, most of the work in this area is experimental. This paper aims to contribute to a more complete understanding, by providing rigorous analysis. We study the imitation dynamics on two classes of graph: cycles and complete graphs. We focus on three well known social dilemmas, namely the Prisoner's Dilemma, the Stag Hunt and the Snowdrift Game. We also consider, for completeness, the so-called Harmony Game. Our analysis shows that, on the cycle, all four games converge fast, either to total cooperation or total defection. On the complete graph, all but the Snowdrift game converge fast, either to cooperation or defection. The Snowdrift game reaches a metastable state fast, where cooperators and defectors coexist. It will converge to cooperation or defection only after spending time in this state which is exponential in the size, n, of the graph. In exceptional cases, it will remain in this state indefinitely. Our theoretical results are supported by experimental investigations.Comment: 32 page

    Imitation in Large Games

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    In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types

    Evolutionary stability on graphs

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    Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k > 2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs

    Conformity Hinders the Evolution of Cooperation on Scale-Free Networks

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    We study the effects of conformity, the tendency of humans to imitate locally common behaviors, in the evolution of cooperation when individuals occupy the vertices of a graph and engage in the one-shot Prisoner's Dilemma or the Snowdrift game with their neighbors. Two different graphs are studied: rings (one-dimensional lattices with cyclic boundary conditions) and scale-free networks of the Barabasi-Albert type. The proposed evolutionary-graph model is studied both by means of Monte Carlo simulations and an extended pair-approximation technique. We find improved levels of cooperation when evolution is carried on rings and individuals imitate according to both the traditional pay-off bias and a conformist bias. More important, we show that scale-free networks are no longer powerful amplifiers of cooperation when fair amounts of conformity are introduced in the imitation rules of the players. Such weakening of the cooperation-promoting abilities of scale-free networks is the result of a less biased flow of information in scale-free topologies, making hubs more susceptible of being influenced by less-connected neighbors.Comment: 14 pages, 11 figure

    Asymmetric evolutionary games

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    Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner's Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.Comment: accepted for publication in PLOS Comp. Bio

    Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

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    We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network
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