Regensburg 2016 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 7: Poster
SOE 7.11: Poster
Montag, 7. März 2016, 18:00–20:00, Poster B1
Evolutionary stability of mixed strategies on graphs — Yan Li1, •Jens Christian Claussen2, and Xinsheng Liu1 — 1Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China — 2Computational Systems Biology, Jacobs University Bremen, Germany
Up to the present, the study of evolutionary dynamics mostly focused on pure strategy games in finite discrete strategy space, either in well-mixed or structured populations. In this paper, we study mixed strategy games in continuous strategy space on graphs of degree k. Each player is arranged on a vertex of the graph. The edges denote the interaction between two individuals. In the limit of weak selection, we first derive the payoff functions of two mixed strategies under three different updating rules, named birth-death, death-birth and imitation. Then we obtain the conditions for a strategy being continuously stable strategy (CSS), we also confirm that the equilibrium distribution corresponding to the CSS is neighborhood attracting and strongly uninvadable. Finally we apply our theory to the Prisoner's Dilemma and the snowdrift game to obtain possible CSS. Simulations are performed for the two special games and the results are well consistent with the conclusions.