Information sharing decisions in all-pay auctions with correlated types

In many real-life competitions, contestants may not be aware of their own type (e.g., value or ability) prior to the contest. Furthermore, contestants’ types, which are observed privately after entering the competition, are frequently correlated with one another. We examine a two-stage competition that involves two players with correlated (binary) types. In the first stage, players decide simultaneously or sequentially on the probabilities they use to disclose or conceal their type, which will become their private information later on. In the second stage, each player privately observes their own type and commits to disclosing or concealing it, after which they compete in an all-pay auction. We discover that information sharing does not occur when players’ types are negatively correlated. However, when players’ types are positively correlated, information is partially shared in all equilibria examined in this study. 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.