Evolutionary dynamics of N-person Hawk-Dove games

In the animal world, the competition between individuals belonging to different species for a resource often requires the cooperation of several individuals in groups. Evolutionary Game Theory provides a theoretical framework to model Darwinian competition that has been widely used to study evolving populations of lifeforms in biology and, particularly, for the study of cooperative behavior in animals. In this context, most of the research has focused on two-person games such as the Prisoner’s Dilemma, the Stag Hunt, and the Hawk-Dove Game, which describe conflicting situations where some individuals profit from selfishness to the detriment of others. However, many real-life situations involve collective decisions made by a group, rather than by only two individuals. In this regard, we show that when more than two agents are involved, both Snowdrift and Hawk-Dove problems are different and the conflict underlying both situations can be addressed through different generalizations of two-person games. We propose a generalization of the Hawk-Dove Game for an arbitrary number of agents: the N-person Hawk-Dove Game. In this model, doves exemplify the cooperative behavior without intraspecies conflict, while hawks represent the aggressive behavior. In the absence of hawks, doves share the resource equally and avoid conflict, but having hawks around lead to doves escaping without fighting. Conversely, hawks fight for the resource at the cost of getting injured. Nevertheless, if doves are present in sufficient number (given by a threshold T) to expel the hawks, they can aggregate to protect the resource, and thus avoid being plundered by hawks. The N-person Hawk-Dove game addresses the dilemma where being an aggressive type can reward from interspecies competition but also incur an excessively high cost in intraspecies conflict, or being peaceful type cooperates and aggregates to defend the resource. We derive and numerically solve an exact equation for the evolution of the system in both finite and infinite well-mixed populations, finding the conditions for stable coexistence between both species. Furthermore, by varying the different parameters, we found a scenario of bifurcations that leads the system from dominating hawks and coexistence to bi-stability, multiple interior equilibria and dominating doves.

Authors: 
Wei Chen, Carlos Gracia-Lazaro, Zhiwu Li, Long Wang and Yamir Moreno
Room: 
6
Date: 
Tuesday, September 25, 2018 - 12:45 to 13:00

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