Learning the Type of the Opponent in Imperfectly Discriminating Contests with Asymmetric Information

In a competitive environment players often face uncertainty about the relative strength of their opponents. This paper considers a winner-take-all rent-seeking contest between two players with different costs of effort. Costs of effort are private knowledge, however, players have an opportunity to learn the opponent's type by engaging in either private (the opponent does not know about the information acquisition) or public (the opponent knows about the information acquisition) learning. We show that a situation, when one player learns the type of the opponent privately while the opponent abstains from learning cannot be an equilibrium. Yet, there exists an equilibrium, when one player engages in public learning and the other refrains from learning.