Aspiration, Learning and Social Change

Abstract

We consider the problem of the transition from the Pareto inferior pure strategy Nash equilibrium in the stag hunt game to the Pareto superior equilibrium. We adopt the methodology of learning and evolutionary game theory to analyze this problem. We model the problem as a population game in which agents play a mixed strategy over the two actions—stag and hare. Agents change their strategy according the generalized reinforcement learning rule. Under this rule, each agent carries a common exogenous aspiration parameter. If the current action generates payoff higher than aspiration, the probability of that action increases. If the payoff is lower than aspiration, the probability declines. This learning rule generates the generalized reinforcement dynamic that allows us to track the distribution of agents over the two actions of stag and hare. We then investigate conditions under which the society can shift from the inferior to the superior equilibrium. One conclusion is that a change in the exogenous aspiration level can trigger such a change.