Assignment Messages and Exchanges

"Assignment messages" are maximally general messages to describe substitutable preferences by means of a linear program. With "integer assignment messages," there exist integer-valued Walrasian allocations, extending a result of Lloyd S. Shapley and Martin Shubik (1971). Any pure Nash equilibrium profile of the Walrasian mechanism with participants limited to assignment messages is also a Nash equilibrium of the unrestricted Walrasian mechanism. Assignment exchanges are generalizations of single-product double auctions and are related to ascending multi-product clock auctions and the Vickrey mechanism. Assignment messages also have additional applications in mechanism design. (JEL D44, D82)