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

JAUME D. MASSÓ J. AND NEME A.

Evanston, Illinois. USA.

Congreso; Third World Congress of the Game Theory Society. GAMES 2008; 2008

Northwestern University.

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 different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define 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. We also show that the set of equilibrium price vectors has a natural lattice structure and we study how this structure is translated into the set of agents´ utilities that are attainable at equilibrium.