Assignment Messages and Exchanges

“Assignment messages” are messages that parameterize substitutable preferences using a particular linear program. An “assignment exchange” is a simplified Walrasian exchange in which participants are restricted to report only assignment messages. Any pure Nash or e-Nash equilibrium of the simplified mechanism is a Nash or e-Nash equilibrium of the Walrasian mechanism before simplification. With a further restriction to basic assignment messages, the exchange yields integer-valued allocations, thus generalizing the Shapley-Shubik assignment mechanism. Connections are reported between assignment exchanges and ascending multi-product clock auctions, double auctions for a single product, and Vickrey auctions. Applications include some cases of Leontieff complements.