Monetary Neutrality under Evolutionary Dominance of Bounded Rationality

We provide evolutionary game-theoretic microfoundations to a dynamic complete nominal adjustment in response to a monetary shock. To this end, we develop an approach based on a new analytical notion to which we refer as boundedly rational inattentiveness. We investigate the behavior of the price level in an context in which a firm can either pay a cost to update its information set and establish the optimal price (Nash strategy) or freely use information from the previous period and establish a lagged optimal price (bounded rationality strategy). We devise an evolutionary micro-dynamics that, by interacting to the dynamics of the aggregate variables, determines the co-evolution of the distribution of information-updating strategies in the population of firms and the extent of the nominal adjustment of the general price level to a monetary shock. Although the bounded rationality strategy is the only survivor in the long-run evolutionary equilibrium, money is nonetheless neutral. The evolutionary learning dynamics takes the information-updating process to an equilibrium configuration in which, despite all firms play the bounded rationality strategy, the corresponding price level is the symmetric Nash equilibrium price.