最优迁移促进异质种群合作的爆发
Optimal migration promotes the outbreak of cooperation in heterogeneous populations
摘要：
我们考虑一个人口的代理是异质性的（一）他们的策略时，互动$n_{g}$次与其他代理在迭代囚徒困境游戏，（二）他们的空间位置上$K$不同的岛屿。在每一代之后，代理人采用与他们收到的平均回报成比例的策略。假设两个合作和两个叛逃的策略的混合，我们首先调查孤立的岛屿的条件下，这些策略和它们可能共存的排他性的统治。这允许定义合作的阈值频率，其依赖于$n_{g}$和策略的初始组合，描述在没有迁移的情况下合作的爆发。然后，我们允许在每一代之后迁移固定比例的人口。假设一个最坏的情况下，所有的岛屿都被占领的叛逃策略，而只有一个岛屿被占领的合作者在阈值频率，我们确定的最佳迁移率，允许爆发的合作\emph{all}岛屿。我们进一步发现，阈值频率除以岛屿的数量，即与合作者入侵叛逃岛屿的相对努力与岛屿的数量递减。我们还表明，只有一个小的带宽的迁移率，允许爆发的合作。更高的移民率会破坏合作。
英文摘要：
We consider a population of agents that are heterogeneous with respect to (i) their strategy when interacting $n_{g}$ times with other agents in an iterated prisoners dilemma game, (ii) their spatial location on $K$ different islands. After each generation, agents adopt strategies proportional to their average payoff received. Assuming a mix of two cooperating and two defecting strategies, we first investigate for isolated islands the conditions for an exclusive domination of each of these strategies and their possible coexistence. This allows to define a threshold frequency for cooperation that, dependent on $n_{g}$ and the initial mix of strategies, describes the outbreak of cooperation in the absense of migration. We then allow migration of a fixed fraction of the population after each generation. Assuming a worst case scenario where all islands are occupied by defecting strategies, whereas only one island is occupied by cooperators at the threshold frequency, we determine the optimal migration rate that allows the outbreak of cooperation on \emph{all} islands. We further find that the threshold frequency divided by the number of islands, i.e. the relative effort for invading defecting islands with cooperators decreeses with the number of islands. We also show that there is only a small bandwidth of migration rates, to allow the outbreak of cooperation. Larger migration rates destroy cooperation.
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