The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit 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 …xed number of units. We de…ne a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price We thank Ester Camiña, John Hat…eld, and Alejandro Manelli for their very helpful comments. The work of D. Jaume and A. Neme is partially supported by the Universidad Nacional de San Luis through grant 319502 and by the Consejo Nacional de Investigaciones Cientí…cas y Técnicas (CONICET) through grant PICT-02114. Support for the research of J. Massó was received through the prize “ICREA Acadèmia” for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE, where he is an a¢ liated researcher, and of the Barcelona Graduate School of Economics (through its Research Recognition Programme), where he is an a¢ liated professor. His work is also supported by the Spanish Ministry of Science and Innovation through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya through grant SGR2009-419. yInstituto de Matemática Aplicada de San Luis. Universidad Nacional de San Luis and CONICET. Ejército de los Andes 950. 5700, San Luis, Argentina. E-mails: [email protected] and [email protected] zDepartament d’Economia i d’Història Econòmica and CODE. Universitat Autònoma de Barcelona. 08193, Bellaterra (Barcelona), Spain. E-mail: [email protected]