Equilibrium existence in two-player contests without absolute continuity of information

We prove the existence of a behavioral-strategy Bayesian Nash equilibrium, without assuming absolute continuity of information, in two-player common-value contests where each player’s probability to win is continuous in efforts outside the zero-effort profile and non-decreasing in his own effort. In particular, equilibrium exists even if both players have a continuum of interdependent information types without joint density.