标题： N人鹰鸽博弈的进化动力学 显示英文标题

标题： Evolutionary dynamics of N-person Hawk-Dove games

摘要： 在动物世界中，不同物种的个体之间为资源而进行的竞争通常需要群体中多个个体的合作。 本文提出了一种针对任意数量代理的鹰鸽博弈的推广：多人鹰鸽博弈。 在这个模型中，鸽子代表没有种内冲突的合作行为，而鹰则代表攻击性行为。 在没有鹰的情况下，鸽子平等分享资源并避免冲突，但当有鹰存在时，鸽子会逃避而不战斗。 相反，鹰为了资源而战斗，但会付出受伤的代价。 然而，如果鸽子数量足够多可以驱逐鹰，它们可以聚集起来保护资源，从而避免被鹰掠夺。 我们推导并数值求解了有限和无限混合种群中系统演化的精确方程，找到了两种物种稳定共存的条件。 此外，通过改变不同的参数，我们发现了一个分岔场景，使系统从鹰主导和共存转变为双稳态、多个内部平衡点和鸽子主导。 显示英文摘要

摘要： 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.