Building on recent work on dynamic interactive epistemology, we are able to extend the analysis of psychological games (Geneakoplos, Pearce and Stacchetti, Games and Economic Behavior, 1989, henceforth GPS). In particular, we let psychological payoffs depend not only on initial beliefs, but more generally on conditional beliefs. This has several advantages. First, our framework allows to model dynamic psychological effects (such as sequential reciprocity and psychological forward induction) that are ruled out when epistemic types are identified with hierarchies of initial beliefs. Second, it allows a direct definition and analysis of extensive-form solution concepts, as opposed to the indirect approach adopted in the seminal paper by GPS. We define a notion of psychological sequential equilibrium in beliefs and prove its existence under mild assumptions. We also provide a preliminary exploration of rationalizability. Third, we are able to directly formulate assumptions about “dynamic” rationality and interactive beliefs in order to explore their behavioral implications. Another innovative feature of our analysis is that we allow psychological payoffs to depend on the beliefs of others, as in a state-dependent utility function where the payoff of the decision-maker depends on an unknown state. We argue that several interesting, non-standard interactive situations can be modelled by letting payoffs depend only on the beliefs of the opponents. This approach clearly separates two channels through which beliefs and information affect behavior: the direct (psychological) impact of beliefs on preferences over terminal histories, and the (standard) impact of updated beliefs about the opponents' on the preferences over own stategies.

This is a joint work with Martin Dufwenberg.