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H 2 The evolution of cooperation in an iterated survival game

Auteurs : Wakeley, John (Auteur de la Conférence)
CIRM (Editeur )

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Prisoner’s Dilemma symmetric two-player game deterministic evolutionary models repeated survival games six-state Markov model transient behavior and asymptotics finite population model questions from the audience

Résumé : A new type of a simple iterated game with natural biological motivation is introduced. Two individuals are chosen at random from a population. They must survive a certain number of steps. They start together, but if one of them dies the other one tries to survive on its own. The only payoff is to survive the game. We only allow two strategies: cooperators help the other individual, while defectors do not. There is no strategic complexity. There are no conditional strategies. Depending on the number of steps we recover various forms of stringent and relaxed cooperative dilemmas. We derive conditions for the evolution of cooperation.
Specifically, we describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with simple, unconditional strategies. When both players are present, each step is a symmetric two-player game. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent’s type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit $(n \rightarrow \infty)$. Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner’s Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.

Codes MSC :
91A12 - Cooperative games
91A20 - Multistage and repeated games
91A40 - Game-theoretic models
91A80 - Applications of game theory
92D15 - Problems related to evolution
91A22 - Evolutionary games

Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/Renc1774/Wakeley.pdf

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 10/07/2018
    Date de captation : 27/06/2018
    Collection : Research talks ; Mathematics in Science and Technology ; Probability and Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:48:31
    Domaine : Mathematics in Science & Technology ; Probability & Statistics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-06-27_Wakeley.mp4

Informations sur la rencontre

Nom de la rencontre : Probability and biological evolution / Probabilités et évolution biologique
Organisateurs de la rencontre : Pardoux, Etienne ; Wakolbinger, Anton
Dates : 25/06/2018 - 29/06/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1774.html

Citation Data

DOI : 10.24350/CIRM.V.19418303
Cite this video as: Wakeley, John (2018). The evolution of cooperation in an iterated survival game. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19418303
URI : http://dx.doi.org/10.24350/CIRM.V.19418303

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