“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)
No takes yet. Share an insight, caveat, or question.
Paul Milgrom (2009) studied this question.