We provide evolutionary game‐theoretic microfoundations to a dynamic complete nominal adjustment in response to a monetary shock by introducing a novel analytical notion that we call boundedly rational inattentiveness. We investigate the behavior of the general price level in a context where a firm can either pay a cost (featuring a random component) to update its information set and establish the optimal price (Nash strategy) or freely use non‐updated information and establish a lagged optimal price (bounded rationality strategy). We devise evolutionary microdynamics (with and without mutation) that, by interacting with the dynamics of the aggregate variables, determines the coevolution of the frequency 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. As it turns out, evolutionary learning dynamics take the information‐updating process to a long‐run equilibrium configuration in which, albeit either most or even all firms play the bounded rationality strategy, the general price level is the symmetric Nash equilibrium price and the monetary shocks have persistent, although not permanent, impacts on real output. (JEL E31, C73, D83)