We use evolutionary game theory in order to determinate the long-run behaviours in the monetary policy game. The model we present firstly assumes the government as well as the private sector are boundedly rational players. The behavioral rule of the government is imitation of the best player whereas the public decision follows adaptive expectations. We also question the relevance of the model when the public can make partly rational expectations. In the evolutionary monetary policy game defined, we find that the long-run equilibrium is Pareto-efficient when the government strategic adjustment is lower than the private sector rigidities. This result reflects that the resolution of governments to follow a strategy in the long-run have played a crucial part in the disinflation process, even if this process can generate short-run costs. Under partly rational expectations, it turns out that previous results are not modified, meaning that the results in the Barro-Gordon model further relies on the perfect rationality given to the government rather than on the rational expectations. Moreover, the low inflation strategy turns out to be credible with rational expectations in our model (once this strategy has been experienced as the best one), since the public knows the imitative process gives the low inflation strategy as the right choice.
