Abstract
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.
Highlights
Evolutionary game theory has proved to be a valuable way of modelling behaviour with both animal and human populations (Maynard Smith 1982; Maynard Smith and Price 1973)
Social dilemmas are defined using conditions imposed on the payoff received by a focal individual
These conditions specify the relationship between the payoffs a focal individual receives when its group size and/or composition changes
Summary
Evolutionary game theory has proved to be a valuable way of modelling behaviour with both animal and human populations (Maynard Smith 1982; Maynard Smith and Price 1973). The one considered in Pena et al (2016) is a slight variation to the individual-centred interpretation of Kerr et al (2004) where the effect of cooperation is measured through the change in fitness of individuals rather than the group These papers consider social dilemmas and their properties in detail for a fixed group size; for instance, what is the effect of a change of strategy of a single individual, to the individual and to others in the group? Within human societies, where the most complex interactions take place, examples include the exploitation of natural resources (Kollock 1998) and hunting and the sharing of food in hunter–gatherer societies (Boehm and Boehm 2009) Such general multi-player games have been studied recently (see for example Gokhale and Traulsen (2010), Gokhale and Traulsen (2014) and Broom and Rychtár (2013), Chapter 9). It allows for a more general description of social dilemmas; for example, what is the effect of adding or removing an individual (either a defector or a cooperator) to a group? What is the effect of different group size distributions within a population on the evolution of cooperative behaviour? We consider various examples of social dilemmas that use this interpretation of cooperation, as well as a particular population where group size follows a negative binomial distribution
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