AI 中文总结
本文建模两群体共享递减回报位点的集体搜索，分析招募竞争导致过度招募，使个体收益低于单一群体，并揭示垄断与共存的边界条件。
AI 中文摘要
集体搜索的群体常常通过招募来利用所发现的资源：一个成员将其他成员引导至其发现的位点。招募提高了在已知位点觅食的成员数量，但随着该数量的增长，每个觅食者的回报可能会下降，因此存在一个中间最优招募率。此外，一个位点可能被多个群体使用。在此，我们分析了一个由两个群体组成的模型，它们从单一资源位点觅食，该位点的回报随在场觅食者总数增加而下降。两个群体仅通过这一共享回报相互作用。长期结果要么是两个群体在觅食位点共存，要么是一个群体垄断，我们分析了这两种结果之间的边界。一个群体对其对手的最佳反应并非单调：它随着对手的招募率提高而提高自己的招募率，以试图维持垄断，然后当维持垄断不再最优时，其招募率会不连续地下降。我们分析了模型参数如何控制这一转变：当位点在少量觅食者时即饱和，且对手群体较小时，一个群体放弃垄断。当两个群体规模相当时，存在多个纳什均衡，因此任一群体都可能最终获得较大份额。而当两个势均力敌的群体竞争时，双方的招募率都高于最大化其共同回报的比率，因此每个个体最终获得的回报少于在相同总规模的单一未分裂群体中所能获得的。
英文摘要
Groups that search collectively often exploit what they find by recruiting: one member directs others to a site it has found. Recruitment raises the number of members foraging at a known site, but the return per forager may fall as that number grows, so there is an intermediate optimal recruitment rate. In addition, a site may be used by more than one group. Here we analyze a model of two groups that forage from a single site whose return declines with the total number of foragers present. The two groups interact only through this shared return. The long-run outcome is either coexistence at the foraging site or monopoly by one group, and we analyze the boundary between these two outcomes. A group's best response to its rival is not monotone: it increases its own recruitment rate with the rival's recruitment rate in an attempt to preserve a monopoly, and then its recruitment rate drops discontinuously when it is no longer optimal to preserve a monopoly. We analyze how model parameters govern this shift: a group relinquishes monopoly when the site saturates at few foragers and when the rival group is small. When the two groups have comparable size there are multiple Nash equilibria, so either group may end up with the larger share. And when two equally matched groups compete, both recruit above the rate that maximizes their common return, so that each individual ends with less than it would in a single undivided group of the same total size.
