Contests with private costs: Beyond two players

It was shown previously that in the symmetric contest game of two players, equilibrium bidding is lower in the case of private information than in the case of public information about the players' costs. I consider symmetric contests of an arbitrary number of players with continuously distributed private costs and discuss the existence and properties of equilibrium bidding functions. I show that with more than two players the relationship between equilibrium bids in the cases of public and private information is no longer universal. While high-cost players still bid less in the private information case, relatively low-cost players may bid above or below their corresponding public information bids.