Department of Mathematics, City, University of London, Northampton Square, London, EC1V 0HB, UK.
Department of Mathematical Sciences, The University of Liverpool, Mathematical Sciences Building, Liverpool, L69 7ZL, UK.
Bull Math Biol. 2019 Nov;81(11):4643-4674. doi: 10.1007/s11538-018-00545-1. Epub 2018 Dec 17.
Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games is the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper, we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex.
进化博弈论是一种用于模拟动物和人类行为的重要工具。一类关键的博弈是社会困境博弈，其中合作对群体有利，但在任何群体中，背叛对个体有利。先前的研究已经考虑了哪些博弈可以被归类为社会困境博弈，以及不同类别的困境，但通常集中在固定大小的相互作用群体上。在本文中，我们对所有群体规模的社会困境进行了系统的研究。这允许更丰富的社会困境定义。例如，虽然将群体大小增加到包括另一个背叛者对所有现有成员总是不利的，但额外的合作者可能是好是坏，这取决于特定的困境和群体大小。在这种情况下，我们考虑了一些常用的社会困境，特别是对于由负二项式分布的群体大小组成的种群，展示了群体大小可变性的影响。最引人注目的效果是，增加非阈值公共物品博弈中群体大小的可变性有利于合作的进化。而对于阈值公共物品博弈和公共资源困境，情况则更加复杂。
