A Few Humble Observations on Overconfidence and Equilibrium

This paper describes equilibrium in games where the informed players may be overconfident. Motivated by specific moral-hazard, signalling and screening problems, we first assume that the "uninformed" players know that the "informed" players may be mistaken, but that the "informed" players are unaware of this. In standard bayesian games, we identify a conflict between self-perception and equilibrium conjectures. We thus turn to population games and assume that while each player believes that her own perception is correct, she also knows that the other players in the population are on average overconfident. It is shown that in any equilibrium of anu such game, players cannot be made better-off by being overconfident. Overconfidence may be beneficial only when comparing payoff across different games, or across different equilibria of the same game. The second part of the paper considers any description of high-order knowledge of overconfidence. We determine the descriptions that allow to construct an equilibrium concept immune to introspective conflicts. It is shown that overconfidence cannot make any player better off also in the case that she is aware that the opponents think that she might be overconfident. The paper is concluded by showing how to translate our knowledge-based analysis in the language of Mertens and Zamir (1985) universal types.