Two-Object Two-Bidder Simultaneous Auctions

Symmetric equilibria are constructed for a class of symmetric auction games. The games all have two identical bidders bidding in two simultaneous sealed-bid auctions for identical objects. Information is complete and the objects are either complements or substitutes. In both cases a continuum of mixed-strategy equilibria are identified. All these equilibria have a surprising structure: The supports of all the mixtures that generate equilibria are two one-dimensional curves, and they surround a two-dimensional set of pure best responses.