Three-object two-bidder simultaneous auctions: chopsticks and tetrahedra

Symmetric equilibria are constructed for a class of symmetric auction games. The games all have two identical bidders bidding in three simultaneous first-price sealed-bid auctions for identical objects. Information is complete and the bidders' marginal valuations increase for the second object and then decrease for the third. In all cases the support of the mixture that generates the equilibrium is two-dimensional, and it surrounds a three-dimensional set of best responses. This appears to be a previously unknown structure. (C) 2003 Elsevier Science (USA). All rights reserved.