Dresden 2014 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 6: Poster Session
SOE 6.10: Poster
Monday, March 31, 2014, 18:00–20:00, P2
N-individual Hawk-Dove games in finite and infinite populations — Binghui Fan1, Xinsheng Liu1,3, •Jens Christian Claussen2,3, and Wanlin Guo1 — 1Nanjing University, China — 2Computational Systems Biology Lab, Research II, Jacobs University Bremen, Germany — 3INB, Universität zu Lübeck, Germany
The Hawk-Dove game has been used to analyze conflicts for resources such as food and habitats. But, in the real world, many contests are activities in which many individuals engage. In this paper, we present an N-individual generalization of the well-known Hawk-Dove game by considering the possible existence of a threshold of the frequency of Hawks in the interacting group above which the Doves get nothing and the Hawks fight for the total resource. When the frequency of Hawks is less than the threshold, the Doves can share a portion of the resource and the hawks fight for the remaining portion. Besides, as the frequency of Hawks increases, the portion of the resource that the Doves can gain decreases sharply according to a nonlinear function. Then we discuss evolutionary dynamics of the N-individual Hawk-Dove games with variation of reasonable range of some significant parameters in both infinite and finite populations. Specially, as for infinite populations, the system will always end up either in full Hawk or in a stable equilibrium where Hawks and Doves coexist. In finite populations, which may exhibit different dynamics, we discuss fixation probabilities and fixation times by analytic and numerical methods. We find that the conditional fixation time exhibits a maximum with respect to the group size or the value-to-cost ratio.