Théorie évolutive des jeux

Résumé

La théorie évolutive des jeux, appelée aussi théorie des jeux évolutionniste, est l'application de la théorie des jeux à l'étude de l'évolution de populations en biologie. Elle définit un cadre de compétitions, de stratégies et d'analyses dans lequel la compétition darwinienne peut être modélisée. Elle a vu le jour en 1973 avec la formalisation par John Maynard Smith et George R. Price des compétitions, analysées en tant que stratégies, et des critères mathématiques qui peuvent être utilisés pour prédire les résultats des stratégies concurrentes. La théorie évolutive des jeux diffère de la théorie classique des jeux en ce qu'elle se concentre davantage sur la dynamique du changement de stratégie, qui est influencée par la fréquence des stratégies compétitives dans la population. La théorie évolutive des jeux a contribué à expliquer les bases des comportements altruistes dans l'évolution darwinienne. Elle a suscité l'intérêt des économistes, des sociologues, des anthropologues et des

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https://fr.wikipedia.org/wiki/Th%C3%A9orie_%C3%A9volutive_des_jeux

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La théorie des jeux est un domaine des mathématiques qui propose une description formelle d'interactions stratégiques entre agents (appelés « joueurs »). Les fondements mathématiques de la théorie m

En théorie des jeux, en psychologie comportementale et en psychologie évolutionniste, une stratégie évolutivement stable ou SES (en anglais, evolutionarily stable strategy ou ESS) est un cas particu

La psychologie évolutionniste, évolutive ou évolutionnaire, parfois nommée évopsy ou évo-psy, est un courant de la psychologie cognitive et de la psychosociologie dont l'objectif est d'expliquer les m

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Coevolution of Synchronization and Cooperation in Costly Networked Interactions

Alberto Antonioni, Alessio Vincenzo Cardillo

Despite the large number of studies on synchronization, the hypothesis that interactions bear a cost for involved individuals has seldom been considered. The introduction of costly interactions leads, instead, to the formulation of a dichotomous scenario in which an individual may decide to cooperate and pay the cost in order to get synchronized with the rest of the population. Alternatively, the same individual can decide to free ride, without incurring any cost, waiting for others to get synchronized to his or her state. Thus, the emergence of synchronization may be seen as the byproduct of an evolutionary game in which individuals decide their behavior according to the benefit-to-cost ratio they accrued in the past. We study the onset of cooperation and synchronization in networked populations of Kuramoto oscillators and report how topology is essential in order for cooperation to thrive. We also display how different classes of topology foster synchronization differently both at microscopic and macroscopic levels.

American Physical Society2017

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Why do individuals make different decisions when confronted with similar choices? This paper investigates whether the answer lies in an evolutionary process. Our analysis builds on recent work in evolutionary game theory showing the superiority of a given type of preferences, homo moralis, in fitness games with assortative matching. We adapt the classical definition of evolutionary stability to the case where individuals with distinct preferences in a population coexist. This approach allows us to establish the characteristics of an evolutionarily stable population. Then, introducing an assortment matrix for assortatively matched interactions, we prove the existence of a heterogeneous evolutionarily stable population in 2x2 symmetric fitness games under constant assortment, and we identify the conditions for its existence. Conversely to the classical setting, we find that the favored preferences in a heterogeneous evolutionarily stable population are context-dependent. As an illustration, we discuss when and how an evolutionarily stable population made of both selfish and moral individuals exists in a prisoner's dilemma. These findings offer a theoretical foundation for the empirically observed diversity of preferences among individuals.

2018

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Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

Yannick Rochat

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures.

Public Library of Science2012

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