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# Documents  91A20 | enregistrements trouvés : 4

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## The evolution of cooperation in an iterated survival game Wakeley, John | CIRM H

Post-edited

Mathematics in Science and Technology;Probability and Statistics

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.
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 ...

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## A first course on zero-sum repeated games Sorin, Sylvain | Springer 2002

Ouvrage

- 204 p.
ISBN 978-3-540-43028-5

Mathématiques & applications , 0037

Localisation : Collection 1er étage

théorie des jeux # jeu à deux personnes # jeu aléatoire # jeu stochastique # jeu répété # jeu à information incomplète # théorème minimax

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## Advances in dynamic game theory :numerical methods, algorithms, and applications to ecology and economics Jorgensen, Steffen ; Quincampoix, Marc ; Vincent, Thomas L. | Springer 2007

Ouvrage

- 717 p.
ISBN 978-0-8176-4399-7

Annals of the international society of dynamic games , 0009

théorie des jeux dynamiques # jeux coopératifs et non coopératifs # jeux stochastiques # jeux d'évolution # jeux différentiels # jeux de poursuite # application de la théorie des jeux à l'économie # modèles théoriques # méthodes numériques

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## Nonnegative matrices and applications Bapat, R. B. ; Raghavan, T. E. S. | Cambridge University Press 2009

Ouvrage

- xiii; 336 p.
ISBN 978-0-521-11866-8

Encyclopedia of mathematics and its applications , 0064

Localisation : Collection 1er étage

matrice positive # algèbre linéaire # matrice # matrice stochastique # chaîne de Markov # modèle économique

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