The evolution of fairness under an assortative matching rule in the ultimatum game

This paper studies how a matching rule affects the evolution of fairness in the ultimatum game. Gale et al. (Games Econ Behav 8: 56–90, 1995) show that under the random matching rule, a partially fair imperfect Nash equilibrium in which all proposers are fair but some responders are selfish is asymptotically stable in the limit as noise in learning vanishes if responders are noisier than proposers. This paper shows that, under an assortative matching rule, a mutually fair imperfect Nash equilibrium in which all proposers are fair and all responders are reciprocal is limit asymptotically stable as noise due to committed agents vanishes.