Optimal Belief Equilibrium

We propose a conceptual framework to study motivated beliefs in strategic settings. We consider static games in which players' utilities depend directly on their beliefs about others' actions. We introduce Optimal Belief Equilibrium (OBE), in which each player jointly chooses an action and a belief that justifies that action so as to maximize his belief-based utility given opponents' play. We characterize OBE through an auxiliary game and establish existence in finite games. As a leading case, we focus on anticipatory utility, where players value both realized and anticipated material payoffs. We analyze how equilibrium behavior varies with the intensity of anticipatory motives in several broad classes of games: coordination games, public-good contribution games, centipede games, and cheap talk. We show that optimistic beliefs about others' behavior can facilitate efficient coordination, encourage free-riding, sustain trust-based relationships, and make communication persuasive despite transparent conflicts of interest.