Semi-Infinite Assignment Problems and Related Games

CentER Discussion Paper Series No. 1999-74

Posted: 7 Mar 2000

See all articles by Natividad Llorca

Natividad Llorca

Miguel Hernandez University

Stef H. Tijs

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research; Università degli Studi di Genova - Dipartimento di Matematica

Judith Timmer

University of Twente - Department of Applied Mathematics

Abstract

In 1972 Shapley and Shubik introduced assignment games associated to finite assignment problems in which two types of agents were involved and they proved that these games have a non-empty core. In this paper we look at the situation where the set of one type is infinite and investigate when the core of the associated game is non-empty. Two infinite programming problems arise here, which we tackle with the aid of finite approximations. We prove that there is no duality gap and we show that the core of the corresponding game is non-empty. Finally, the existence of optimal assignments is discussed.

JEL Classification: C70

Suggested Citation

Llorca Pascual, Natividad and Tijs, Stef H. and Timmer, Judith, Semi-Infinite Assignment Problems and Related Games. CentER Discussion Paper Series No. 1999-74, Available at SSRN: https://ssrn.com/abstract=199906

Natividad Llorca Pascual

Miguel Hernandez University ( email )

Operations Research Center (CIO)
Avda. de la Universidad, s/n, Torretamarit
03202 Elche, Alicante
Spain

Stef H. Tijs

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
B925
5000 LE Tilburg
Netherlands
+31 13 466 2348 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Università degli Studi di Genova - Dipartimento di Matematica

Via Dodecaneso 35
16146 Genoa
Italy

Judith Timmer (Contact Author)

University of Twente - Department of Applied Mathematics ( email )

P.O. Box 217
7500 AE Enschede
Netherlands

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