Play and the evolution of fairness: a game theory model

Bekoff [J. Consci. Stud. 8 (2001) 81] argued that mammalian social play is a useful behavioral phenotype on which to concentrate in order to learn more about the evolution of fairness. Here, we build a game theoretical model designed to formalize some of the ideas laid out by Bekoff, and to examine whether 'fair' strategies can in fact be evolutionarily stable. The models we present examine fairness at two different developmental stages during an individual's ontogeny, and hence we create four strategies-fair at time 1/fair at time 2, not fair at time 1/not fair at time 2, fair at time 1/not fair at time 2, not fair at time 1/fair at time 2. Our results suggest that when considering species where fairness can be expressed during two different developmental stages, acting fairly should be more common than never acting fairly. In addition, when no one strategy was evolutionarily stable, we found that all four strategies we model can coexist at evolutionary equilibrium. Even in the absence of an overwhelming database from which to test our model, the general predictions we make have significant implications for the evolution of fairness.