Equilibrium Selection by Intentional Idiosyncratic Play

We introduce intentional idiosyncratic play in a standard stochastic evolutionary model of equilibrium selection in bargaining games. We define intentional mutations as rare play of mixed strategies that are supported only on the set of strategies that would give the idiosyncratic player a higher payoff were sufficiently many others to do the same. In contract games intentional idiosyncratic play alters the standard perturbed evolutionary dynamic, where idiosyncratic play is drawn from the entire strategy set, in ways that are plausible in light of historical studies of institutional transitions. First, the most probable transitions between institutions are induced only by the idiosyncratic play of those who stand to benefit from the switch. Second, where sub-population sizes and idiosyncratic play rates differ cross groups, the group whose interests are favored are those who engage in more frequent idiosyncratic play and who are are less numerous. The intentional idiosyncratic play dynamic selects the equilibrium that implements the Nash bargain as the stochastically stable state, while the standard dynamic selects the Kalai-Smorodinsky bargain.