Department of Mathematics, University of British Columbia, Vancouver B.C. V6T 1Z2, Canada.
Department of Zoology, University of British Columbia, Vancouver B.C. V6T 1Z4, Canada.
J R Soc Interface. 2024 Oct;21(219):20240334. doi: 10.1098/rsif.2024.0334. Epub 2024 Oct 30.
When individuals interact in groups, the evolution of cooperation is traditionally modelled using the framework of public goods games. These models often assume that the return of the public goods depends linearly on the fraction of contributors. In contrast, in real-life public goods interactions, the return can depend on the size of the investor pool as well. Here, we consider a model in which the multiplication factor (marginal per capita return) for the public goods depends linearly on how many contribute, which results in a nonlinear model of public goods. This simple model breaks the curse of dominant defection found in linear public goods interactions and gives rise to richer dynamical outcomes in evolutionary settings. We provide an in-depth analysis of the more varied decisions by the classical rational player in nonlinear public goods interactions as well as a mechanistic, microscopic derivation of the evolutionary outcomes for the stochastic dynamics in finite populations and in the deterministic limit of infinite populations. This kind of nonlinearity provides a natural way to model public goods with diminishing returns as well as economies of scale.
当个体在群体中相互作用时，合作的演化传统上是使用公共物品博弈的框架来建模的。这些模型通常假设公共物品的回报与贡献者的比例线性相关。相比之下，在现实生活中的公共物品互动中，回报也可能取决于投资者群体的规模。在这里，我们考虑一个模型，其中公共物品的倍增因子（人均边际回报）与贡献者的数量线性相关，这导致了公共物品的非线性模型。这个简单的模型打破了线性公共物品相互作用中占主导地位的缺陷，在进化环境中产生了更丰富的动态结果。我们深入分析了经典理性参与者在非线性公共物品相互作用中的更多不同决策，并对有限群体中的随机动力学和无限群体的确定性极限中的进化结果进行了机械的、微观的推导。这种非线性为具有递减回报和规模经济的公共物品提供了一种自然的建模方式。
