Existence of Equilibrium in Single and Double Private Value Options

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated and asymmetrically distributed. For double auctions, we show further that at least one equilibrium involves a positive volume of trade. The existence proof establishes new connections among existence techniques for discontinuous Bayesian games.