Competitive Equilibrium Always Exists for Combinatorial Auctions with Graphical Pricing Schemes

Abstract We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive easy-to-construct class of can model both complementarity substitutes, to our knowledge, it the first besides gross substitutes have guaranteed equilibrium. prove through counter-examples result tight, we give explicit algorithms for constructing pricing vectors. also extensions multi-unit (also known as product-mix auctions). Combined theorems on Candogan, Ozdagar Parrilo, results indicate quadratic highly practical method run auctions.