Nash Equilibria in Combinatorial Auctions with Item Bidding by Two Bidders

Abstract

We discuss Nash equilibria in combinatorial auctions with item bidding. Specifically, we give a characterization for the existence of a Nash equilibrium in such a combinatorial auction when valuations by two bidders satisfy symmetric and subadditive properties. Based on this characterization, we can obtain an algorithm for deciding whether a Nash equilibrium exists in such a combinatorial auction.