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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 8: Economic Models and Evolutionary Game Theory

AKSOE 8.2: Talk

Tuesday, February 26, 2008, 10:45–11:15, EW 203

Cooperation in Prisoner's Dilemma with Dynamical Connection Weights — •Platkowski Tadeusz and Mogielski Krzysztof — Department of Mathematics, Informatics and Mechanics, University of Warsaw

We propose a model of continuous population of agents which, at any instant of time, are randomly matched to play the 2-person Prisoner's Dilemma game. The payoff from each encounter depends on the payoff matrix and on the weights of connections between different types of players. In our model the weights are dynamical variables. Their evolution depends on the difference of the agent's payoff from the considered type of encounters and his average payoff. Time evolution of the frequency of cooperators in the population is governed by the replicator equation. Both symmetric and asymmetric weights between cooperators and defectors are considered. Solutions of the resulting systems of differential equations are discussed. Structure of equilibrium states of the systems is investigated. In particular we prove existence of equilibrium states with partial cooperation.