Selective memory of a psychological agent

We consider a single psychological agent whose utility depends on his action, the state of the world, and the belief that he holds about that state. The agent is initially informed about the state and decides whether to memorize it, otherwise he has no recall. We model the memorization process by a multi-self game in which the privately informed first self voluntarily discloses information to the second self, who has identical preferences and acts upon the disclosed information. We identify broad categories of psychological utility functions for which there exists an equilibrium in which every state is voluntarily memorized. In contrast, if there are exogenous failures in the memorization process, then the agent memorizes states selectively. In this case, we characterize the partially informative equilibria for common classes of psychological utilities. If the material cost of forgetting is low, then the agent only memorizes good enough news. Otherwise, only extreme news are voluntarily memorized.