“Spying in Contests”

Zhuoqiong Chen, London School of Economics

Two players compete for a prize and their valuations are private information. Before the contest, each player can covertly acquire a costly, noisy and private signal regarding the opponent's valuation. In equilibrium, each player's effort is non-decreasing (non-increasing) in the posterior probability that the opponent has the same (a different) valuation. Accounting for the cost of spying, players are strictly better off than not spying on each other at all. Suppose instead that without incurring any cost to any player, each player can ex ante commit to disclose a signal about her valuation to the opponent, but cannot observe realizations of the signal. Then there does not exist any equilibrium in which both players disclose an informative signal to the opponent, even though doing so would benefit both players.