The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria

Abstract: A multiple-partners assignment game with heterogeneous sells and multi-unit demands consists of a set of sellers that own a given number of indivisible units of (potentially many di¤erent) goods and a set of buyers who value those units and want to buy at most an exogenously \u85xed number of units. We de\u85ne a competitive equilibrium for this generalized assignment game and prove its existence using linear programming. We show that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all equilibrium assignments, and vice versa