Solving Combinatorial Exchanges: Optimality via a Few Partial Bids

Abstract

Auctions have been studied in economics and game theory for a long time as important resource allocation mechanisms in distributed environments. In recent years, their role has grown with the emergence of Internet and electronic commerce, as businesses and corporations leverage the new medium to streamline their procurement process. Many businesses are moving to an auction-based purchase method where they issue a request for quotes for the goods and services needed, and let the suppliers bid for a piece of the business. Driven by these fundamentals, auctions and algorithms related to them have become important and popular research topics in computer science. An exchange generalizes the auction mechanism to the setting with multiple buyers and sellers. Some familiar examples are the exchanges for equities and commodities, transportation, electricity, and the businessto-business exchanges. A combinatorial exchange is an exchange where buyers and sellers can bid on bundles (subsets) of goods. Combinatorial markets are desirable because items often have complementarity, and combinatorial bidding minimizes bidders’ risk of getting stuck with only a partial subset. It also improves the overall economic efficiency.