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Zoological Research
Kunming Institute of Zoology, Chinese Academy of Sciences
ISSN: 2095-8137
Vol. 33, No. 4, 2012, pp. 373-380
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Bioline Code: zr12059
Full paper language: English
Document type: Research Article
Document available free of charge
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Zoological Research, Vol. 33, No. 4, 2012, pp. 373-380
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Evolutionary stability analysis of asymmetric hawk-dove game considering the impact of common resource
LIU, Qi-Long; HE, Jun-Zhou; YANG, Yan; WANG, Ya-Qiang; GAO, Lei; LI, Yao-Tang & WANG, Rui-Wu
Abstract
Explaining the evolution of cooperation remains one of the important problems in both biology and social
science. Classical theories mainly based on an assumption that cooperative players are symmetrically interacted. However,
almost all the well-studied systems showed that cooperative players are in fact asymmetrically interacted and that
asymmetric interaction might greatly affect cooperation behavior of the involved players. Considering the asymmetric
interaction and the selection pressure of resources, we present a model that possesses four strategies: strengthcooperation
(SC), strength-defection (SD), weakness-cooperation (WC) and weakness-defection (WD). Combining
evolutionary game theory with dynamical stability theory, we find that the evolutionary results closely depend on the
asymmetric interaction and selection pressure of resources as well as cost-to-benefit ratio of conflict. When the common
resources are plentiful, the cost-to-benefit ratio of conflict is negatively correlated with the probability of SC, while it is
positively correlated with the probability of SD and WD. With increasing the strength ratio between the strong and weak
players, the proportion of SC and SD will increase, while the proportion of WD will reduce. The model developed here has
intrinsically integrated Boxed Pigs game and Hawk-Dove game. When the common resource is at shortage, the Boxed Pigs
game will transform into Hawk-Dove game under the increase of the strength ratio between the strong and weak players.
Keywords
Asymmetric; Hawk-Dove game; Replicator equation; Evolutionarily stable strategy; Boxed pigs game
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