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A Note on Bayesian Nash Equilibria in Imperfectly Discriminating Contests

The literature on imperfectly discriminating contests has almost exclusively focused on complete information. We study such contests assuming players have private information. We identify a general class of imperfectly discriminating contests for which findings by Athey (2001) imply the existence of a Bayesian Nash equilibrium in monotone pure strategies. The main assumptions are that a player’s valuation of winning is increasing in the signal he observes and that a player’s probability of winning is continuous in the efforts of all players as well as increasing in his own effort.