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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 7: Economic Models and Evolutionary Game Theory I

AKSOE 7.2: Talk

Tuesday, March 27, 2007, 10:45–11:15, H8

Game dynamics in finite populations — •Arne Traulsen — Program for Evolutionary Dynamics, Harvard University, USA

For the study of evolutionary game dynamics in finite populations, the Fermi function from statistical physics is chosen to govern strategy changes. The inverse temperature controls the intensity of selection, leading from random drift to imitation dynamics. This framework results in a closed analytical expression for the probability that a certain type will take over the population [1]. In this process, one can also relax the usual assumption that two individuals of the same type have the same fitness. Instead, each individual has a randomly distributed number of interactions with other individuals. This increases the temperature of selection [2]. Finally, the process can be utilized to describe limiting cases of games on dynamical networks. We assume that individuals differ in the rate at which they seek interactions. Links are formed and broken off accoring to their productivity. If this active linking process is fast compared to strategy changes, it introduces a simple transformation of the payoff matrix [3]. For slow active linking, the system is equivalent to strategy dynamics on a static network. For intermediate ranges, a numerical investigation of the detailed interplay determined by these two time-scales shows that the analytical results extends to a much wider ratio of time scales than expected [4].

[1] Traulsen, Nowak, and Pacheco, Phys.Rev.E 74, 11909 (2006).

[2] Traulsen, Nowak, and Pacheco, J.Theor.Biol., 244, 349 (2007).

[3] Pacheco, Traulsen, and Nowak, J.Theor.Biol. 243, 437 (2006).

[4] Pacheco, Traulsen, and Nowak, Phys.Rev.Lett., in press.