Spying in Contests

Two players with independent private values compete for a prize in an all-pay contest. Before the contest, each player can spy on the opponent by privately acquiring a costly, noisy, and private signal about his private value. In a symmetric equilibrium of the contest where players spy on each other, the equilibrium effort to compete for the prize is non-decreasing in the posterior probability that the opponent has the same value. Such an equilibrium is efficient if and only if the spying signals acquired are sufficiently inaccurate. Accounting for the cost of spying, players are better off spying than not spying at all