Title: Evolutionary dynamics of N-person Hawk-Dove games,
Abstract: In the animal world, the competition between individuals belonging to
different species for a resource often requires the cooperation of several
individuals in groups. This paper proposes 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 to expel the hawks, they can aggregate to protect the resource, and thus
avoid being plundered by hawks. 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.