Evolutionary dynamics of group fairness

The emergence and impact of fairness is commonly studied in the context of 2-person games, notably the Ultimatum Game. Often, however, humans face problems of collective action involving more than two individuals where fairness is known to play a very important role, and whose dynamics cannot be inferred from what is known from 2-person games. Here, we propose a generalization of the Ultimatum Game for an arbitrary number of players - the Multiplayer Ultimatum Game. Proposals are made to a group of responders who must individually reject or accept the proposal. If the total number of individual acceptances stands below a given threshold, the offer will be rejected; otherwise, the offer will be accepted, and equally shared by all responders. We investigate the evolution of fairness in populations of individuals by means of evolutionary game theory, providing both analytical insights and results from numerical simulations. We show how imposing stringent consensuses significantly increases the value of the proposals, leading to fairer outcomes and more tolerant players. Furthermore, we show how stochastic effects - such as imitation errors and/or errors when assessing the fitness of others - may further enhance the overall success in reaching fair collective action.