Coevolution of fairness and spite on stochastic dynamics networks

Abstract

The evolution of fairness is favored by adaptive social structures, yet it is infeasible to give precise solutions of how to adjust social ties to optimize the evolution of fairness. This study establishes linking dynamics by stochastic process for coevolutionary fairness, and introduces a key ratio between the probability of rewiring for accepting offers and that for rejecting offers. We demonstrate that there exists an optimum interval of ratio for the domination of fairness, and the introduction of spiteful strategy can relax this condition to favor fairness. Moreover, the ratio below the optimum drives the state space to evolve into two attractors of being either fair or unfair, whereas a too high ratio allows the mutual invasion between fairness and unfairness. Our results reveal that the condition for the domination of fairness requires a moderate negative assortments, which provides a potential way to understand the evolutionary fairness in human society.