Evolution of fairness in the mixture of the Ultimatum Game and the Dictator Game

The Ultimatum Game characterizes the scheme to split a sum of money between the proposer and the responder. Both players benefit from the successful allocation whenever the scheme presented by the proposer is endorsed by the responder, yet both receive nothing otherwise. Meanwhile, the responder in the Dictator Game has no choice but to accept what is offered by the proposer. As both games may occur in some realistic situations, we study the population dynamics by considering the mixture of the Ultimatum Game and the Dictator Game. Mixture means a fraction of individuals play the Dictator Game with their partners while others play the Ultimatum game. We introduce degree-related assignment rules to determine who shall play the Dictator Game in the heterogeneous populations. Our results show that the evolution of fairness can be promoted by assigning an appropriate fraction of hubs to be dictators, a novel finding deviating from the subgame perfect Nash equilibrium where proposers tend to leave next to nothing to their responders. Our work highlights the importance of network reciprocity in enhancing the evolution of fairness. (C) 2018 Elsevier B.V. All rights reserved.