标题： 公共物品博弈的制度激励复制-变异动力学 显示英文标题

标题： Replicator-mutator dynamics for public goods games with institutional incentives

摘要： 理解公共品博弈中合作的出现与稳定性对于生物学、经济学和社会科学等领域具有重要意义。然而，目前仍存在一个理解上的空白，即加性和乘性突变以及制度激励如何影响这些动态过程尚不清楚。 本文研究了公共品博弈中，在存在或不存在制度激励的情况下，带有加性和乘性突变的复制-突变动力学模型。对于每个模型，我们确定可能存在的（稳定的）均衡点数量，展示它们的可达性，并分析其稳定性属性。 我们还通过分岔分析和渐近行为来刻画这些均衡点对模型参数的依赖关系。 我们的研究结果为制度激励的作用以及加性和乘性突变对公共品博弈中合作演化的综合影响提供了严谨且量化的见解。 显示英文摘要

摘要： Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both additive and multiplicative, as well as institutional incentives, influence these dynamics. In this paper, we study the replicator-mutator dynamics, with combined additive and multiplicative mutations, for public goods games both in the absence or presence of institutional incentives. For each model, we identify the possible number of (stable) equilibria, demonstrate their attainability, as well as analyse their stability properties. We also characterise the dependence of these equilibria on the model's parameters via bifurcation analysis and asymptotic behaviour. Our results offer rigorous and quantitative insights into the role of institutional incentives and the effect of combined additive and multiplicative mutations on the evolution of cooperation in the context of public goods games.