Social Sciences Brown Bag Seminar

In a game with uncertainty, there is common knowledge of payoff structure but not the distribution of uncertain parameters, i.e., types. Under these assumptions, equilibrium is defined in terms of the objective outcome of the game (the objective distribution over uncertain parameters and the profile of players' strategies), and supporting players' subjective assessments of the outcome: each player behaves optimally given his assessment and each player's assessment is minimally consistent with the objective outcome and with all other players' assessments. If a player collects a private dataset of infinitely many realizations of own type, action, and payoff received in equilibrium, a player faces an identification problem vis-a-vis the objective outcome. Minimal consistency is the requirement that the player's assessment satisfies limit consistency with such a dataset, and is thus the weakest criterion that admits an interpretation of equilibrium as a steady state of a one-shot-game. Equilibrium is then characterized as a common belief in optimal behavior and minimal consistency. Natural applications are to environments with moral hazard and adverse selection without assuming that players have a common prior, that is, that players were able to correctly identify the true objective uncertainty in the face of identification problems pertinent to such environments. While players' supporting assessment need not be identical to the truth and need not coincide, not every assessment (and hence belief) is admissible as such assessments are still bound by the data generated by the equilibrium play.