Overconfidence, underconfidence, and entry in contests

This paper provides a theoretic foundation for overconfidence driving entry into competition and underconfidence leading to avoidance. We do this using the classic Tullock rent‐seeking contest, modeling overconfidence as an overestimate of one's probability of success and underestimate of an opponent's probability of success and underconfidence as an underestimate of one's probability of success. When an unknowingly overconfident player 1 who overestimates his winning probability faces an unbiased opponent who is aware of player 1's overconfidence, player 1 exerts more effort than player 2, and player 1's objective expected payoff is greater than player 2's. On the other hand, when an unknowingly overconfident player 1 who underestimates his opponent's winning probability faces this unbiased opponent who is aware of player 1's overconfidence, both players reduce their effort and player 1's objective expected payoff is lower than player 2's. However, player 1's subjective expected payoff, which governs entry into the contest, is higher than player 2's, and overconfident players find contests more appealing than unbiased players do, even unbiased players facing other unbiased players. Underconfident players have subjective expected payoffs that are even lower than their objective expected payoffs, so underconfident players tend to avoid competition. The data generated from repeated contests would make it harder for underconfident players to learn of their bias than overconfident ones.