Random Allocations of Multiple Objects with Incomplete Information

By Xu LANG and Zaifu YANG
Forthcoming in Journal of Economic Theory

Abstract:

We propose a condition under which a system of linear inequalities can be found to characterize ex post and interim allocation mechanisms that assign multiple heterogeneous indivisible objects to many agents and also satisfy complex distributional constraints in an incomplete information environment. This condition is called total unimodularity, a well-recognized and rich class of matrices whose entries are, 0, or 1. The condition is so general as to extend and unify a number of well-known results, offer new and general results, and cover such as hierarchies, bihierarchies, adjacency, dependence chains, M♮-concavity, 1-substitutes, and paramodularity. We also provide several applications of practical interest.