Random allocation of pies promotes the evolution of fairness in the Ultimatum Game

In the Ultimatum Game, two players are offered a chance to win a pie. The proposer suggests how to split the pie. The responder can either accept or reject the deal. If an agreement is not reached, neither player gets anything. Both game theory and evolutionary game theory predict the rational solution that the proposer offers the smallest possible share and the responder accepts it. Fairness thus requires additional mechanisms for natural selection to favor it. Studies to date assumed that individuals have competed for the fixed size of pies, in sharp contrast with real situations, where randomness is ubiquitous. Here we study the impact of random allocation of pies on the evolution of fairness in the Ultimatum Game. Interestingly, we find that the evolution of fairness can be promoted by the randomness associated with the size of pies, without the support of any additional evolutionary mechanisms.