弱选择下空间公共物品博弈的惯性
Inertia in spatial public goods games under weak selection
摘要：
由于知觉错误或其他情绪原因，有限的认知技能，球员可能会保持他们目前的策略，即使有一个更有希望的选择。这种行为惯性已经被研究过了，但是在弱选择限制下，它的结果仍然没有被探索。为了填补这一空白，我们考虑了一个空间公共物品博弈模型，在模仿过程中考虑惯性。通过使用身份下降的方法，我们提出了分析形式的关键协同因素$r^\star$，它决定了合作时，是有利的。我们发现，惯性阻碍合作，这可以解释为弱选择下的减速粗化过程。有趣的是，不同的更新协议，包括死亡出生和出生死亡规则的关键协同条件，可以正式联系的惯性因子的极端限制。为了探索我们的观测结果的鲁棒性，计算了不同的晶格和组大小。蒙特卡罗模拟也证实了这一结果。
英文摘要：
Due to limited cognitive skills for perceptual error or other emotional reasons, players may keep their current strategies even if there is a more promising choice. Such behavior inertia has already been studied, but its consequences remained unexplored in the weak selection limit. To fill this gap, we consider a spatial public goods game model where inertia is considered during the imitation process. By using the identity-by-descent method, we present analytical forms of the critical synergy factor $r^\star$, which determines when cooperation is favored. We find that inertia hinders cooperation, which can be explained by the decelerated coarsening process under weak selection. Interestingly, the critical synergy conditions for different updating protocols, including death-birth and birth-death rules, can be formally linked by the extreme limits of the inertia factor. To explore the robustness of our observations, calculations are made for different lattices and group sizes. Monte Carlo simulations also confirm the results.
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