Existence of Equilibria in Auctions with Interdependent Values: Two Symmetric Bidders

For two symmetric bidders, weak monotonicity conditions are shown to imply existence of an equilibrium in mixed behavioral strategies for a sealed-bid first-price auction of an item for which each bidder’s value depends on every bidder’s observed signal. Such an equilibrium has atomless distributions of bids and thus is unaffected by how tied bids are resolved.