Information Sharing Decisions in All-Pay Auctions With Correlated Types

In many real-life contests, contestants do not know their own type (e.g., value or ability) prior to a competition; and contestants’ types, which are observed privately once entering the contest, are often correlated with each other. We study a two-stage contest in which two players with correlated (binary) types are involved. In stage 1, players simultaneously or sequentially decide on their probabilities to disclose/conceal their type, which will become their private information later on. In stage 2, each player observes his own type privately and discloses/conceals his type as committed; after that, they compete in an all-pay auction. We find that information sharing does not occur if players’ types are negatively correlated; if players’ types are positively correlated, information are partially shared in all equilibria studied in this paper. In an asymmetric pure strategy equilibrium, one player shares his information with probability one and the other player with probability zero; in a symmetric mixed strategy equilibrium, each player shares his information with the same positive probability