Learning to be fair in multiplayer Ultimatum Games

We study a multiplayer extension of the well-known Ultimatum Game (UG) through the lens of a reinforcement learning algorithm. Multiplayer Ultimatum Game (MUG) allows us to study fair behaviors beyond the traditional pairwise interaction models. Here, a proposal is made to a quorum of Responders, and the overall acceptance depends on reaching a threshold of individual acceptances. We show that learning agents coordinate their behavior into different strategies, depending on factors such as the group acceptance threshold and the group size. Overall, our simulations show that stringent group criteria trigger fairer proposals and the effect of group size on fairness depends on the same group acceptance criteria.This research was supported by Fundacao para a Ciencia e Tecnologia (FCT) through grants SFRH/BD/94736/2013, PTDC/EEI-SII/5081/2014, PTDC/MAT/STA/3358/2014 and by multi-annual funding of CBMA and INESC-ID (under the projects UID/BIA/04050/2013 and UID/CEC/50021/2013 provided by FCT).