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.
neither a hawk nor a dove book download
Furthermore, as a refinement of the model, we consider the situation in which the doves aggregate to defend the resource, not at all cost, but only in the case they are present in sufficient number to expel the hawks, i.e., there is a minimum threshold T that assures them to succeed. In that case, after expelling the hawks, paying a cost c D for it, doves share the resource without fighting among themselves. Otherwise, i.e., if the number of doves is below the threshold, they retreat and the hawks fight among themselves. It is worth noticing that although both hawks and doves can fight, a hawk will fight in any situation (unless all his opponents flee), while doves only fight against opposite strategists, and provided they are allowed to expel them. This refinement of the model, hereafter N-person HDG with threshold (HDG-T), captures the stress between gregarious and asocial behaviors. We show that, depending on the values of the parameters, the dynamics drives the system towards either one of the absorbing mono-strategic states (all hawks or all doves), or towards an interior equilibrium in which both strategies coexist. Subsequently, we study the dynamics in finite populations, finding results compatible with those obtained for the infinite size limit.
Although two-person Hawk-Dove Games can mathematically be regarded as a Snowdrift Game, this equivalence breaks down when generalizing it to N persons. An N-person Snowdrift Game characterizes real-world situations in which a task needs to be done by cooperating, with the consequent benefit for the group, whereas the proposed model describes the competition for a resource between two species. The N-person Hawk-Dove here presented thus conceptualizes the dilemma that being an aggressive type can reward from interspecies competition but also incurs a high cost in terms of intra-species conflict, while cooperators aggregate and share the resource. We also hypothesize that, if the present model were to be applied to a real context in nature, the threshold needed for successful preservation of the doves type would be very high. Indeed, a high threshold is more realistic than the assumptions on which either doves obtain nothing unless no hawks are in the group or a low threshold that implies a fiercer intra-species conflict. Furthermore, group interactions can not be regarded as a set of independent pairwise encounters. Finally, we mention that in previous studies of a two-person Hawk-Dove Game, both an heterogeneous topology and different update rules have been proven to have an impact on cooperation29, 30. It would thus be of further interest to explore how such factors change our findings for N-person hawk-dove games, and therefore gain more insights into our current understanding of cooperative behavior in social dilemmas.
Assuming the Fermi-like rule32, at each elementary time step two individuals are chosen at random from the population. If they are of different species, then the probabilities that a dove replaces a hawk, and the opposite scenario, are given, respectively, as
2ff7e9595c
Comments