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Research talks;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 ...

91A80 ; 91A40 ; 91A22 ; 91A12 ; 91A20 ; 92D15

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ISBN 978-0-7923-8661-2

Theory and decision library series c : game theory, mathematical programming and mathematical , 0023

Localisation : Colloque 1er étage (GENO)

application de la théorie des jeux # partage de coût # politique # économie # équilibre dépense/gain # étude expérimentale

91-06 ; 91A80 ; 91A90

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- x; 339 p.
ISBN 978-1-107-01103-8

Mathematical sciences research institute publications , 0063

Localisation : Colloque 1er étage (BANF)

théorie des jeux # analyse combinatoire

91-06 ; 91A46 ; 91A80 ; 91-04 ; 68W99 ; 00B25

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Research schools;Control Theory and Optimization;Mathematics in Science and Technology

We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzero-sum timing game describing the transitions among the discrete investment stages. Working in a continuous-time diffusion framework, we characterize and analyze the resulting Nash equilibrium and game values. Our analysis quantifies the dynamic competition effects and yields insight into dynamic preemption and over-investment in a general asymmetric setting. A case-study considering the impact of fluctuating emission costs on power producers investing in nuclear and coal-fired plants is also presented. We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzero-sum timing game describing the transitions among the ...

93E20 ; 91B38 ; 91A80

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Research schools;Computer Science;Probability and Statistics

In this talk, I will introduce the classical theory of multi-armed bandits, a field at the junction of statistics, optimization, game theory and machine learning, discuss the possible applications, and highlights the new perspectives and open questions that they propose We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzero-sum timing game describing the transitions among the discrete investment stages. Working in a continuous-time diffusion framework, we characterize and analyze the resulting Nash equilibrium and game values. Our analysis quantifies the dynamic competition effects and yields insight into dynamic preemption and over-investment in a general asymmetric setting. A case-study considering the impact of fluctuating emission costs on power producers investing in nuclear and coal-fired plants is also presented. In this talk, I will introduce the classical theory of multi-armed bandits, a field at the junction of statistics, optimization, game theory and machine learning, discuss the possible applications, and highlights the new perspectives and open questions that they propose We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate ...

62L05 ; 68T05 ; 91A26 ; 91A80 ; 91B26

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- 330 p.
ISBN 978-2-02-033924-7

Science ouverte

Localisation : Ouvrage RdC (MERO)

application # modélisation # philosophie # psychologie # théorie des jeux

00A30 ; 91A80 ; 91AXX ; 91EXX

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- 538 p.
ISBN 978-0-12-532111-2

Pure and applied mathematics , 0141

Localisation : Ouvrage RdC (PERR)

language formel # linguistique # automate # logique # mot infini # mot fini # combinatoire des mots # arbre infini

68Q45 ; 68R15 ; 68-01 ; 68-02 ; 20M35 ; 91A80

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

Annals of the international society of dynamic games , 0009

Localisation : Ouvrage RdC (Adva)

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

91AXX ; 91A05 ; 91A06 ; 91A10 ; 91A12 ; 91A15 ; 91A20 ; 91A22 ; 91A23 ; 91A40 ; 91A50 ; 91A80

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- x; 246 p.
ISBN 978-1-107-69091-2

Localisation : Ouvrage RdC (WELL)

modèle mathématique # jeu mathématique # psychologie

00A30 ; 91-01 ; 91A80

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- xiv; 319 p.
ISBN 978-1-107-09642-4

Localisation : Ouvrage RdC (TAMB)

sécurité informatique # théorie des jeux # modèle mathématique # sécurité internationale

91-06 ; 00B15 ; 91A40 ; 91A80

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- x; 146 p.
ISBN 978-3-0348-0824-8

Oberwolfach seminars , 0044

Localisation : Ouvrage RdC (POSI)

théorie des jeux # analyse combinatoire # théorie de Ramsey # jeu de position # graphe stochastique

91-01 ; 91A24 ; 91A80 ; 05C90

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