Semi-Infinite Assignment Problems and Related Games
AbstractIn 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 investigatewhen 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-74.
Date of creation: 1999
Date of revision:
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Web page: http://center.uvt.nl
Infinite programs; assignment; cooperative games; balancedness;
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-10-04 (All new papers)
- NEP-GTH-1999-10-04 (Game Theory)
- NEP-IND-1999-10-04 (Industrial Organization)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kaneko, Mamoru & Wooders, Myrna Holtz, 1986. "The core of a game with a continuum of players and finite coalitions: The model and some results," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 105-137, October.
- Kaneko, Mamoru & Wooders, Myrna Holtz, 1982.
"Cores of partitioning games,"
Mathematical Social Sciences,
Elsevier, vol. 3(4), pages 313-327, December.
- Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
- Fragnelli, V. & Patrone, F. & Sideri, E. & Tijs, S.H., 1999. "Balanced games arising from infinite linear models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-81035, Tilburg University.
- Tijs, S.H., 1975. "Semi-infinite and infinite matrix games and bimatrix games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154313, Tilburg University.
- Timmer, J.B. & Llorca, N. & Tijs, S.H., 1999. "Games Arising from Infinite Production Situations," Discussion Paper 1999-57, Tilburg University, Center for Economic Research.
- Sánchez-Soriano, J. & Llorca, N. & Tijs, S.H. & Timmer, J.B., 2000. "On the Core of Semi-Infinite Transportation Games with Divisible Goods," Discussion Paper 2000-89, Tilburg University, Center for Economic Research.
- Sánchez-Soriano, J. & Llorca, N. & Tijs, S.H. & Timmer, J.B., 2000. "Semi-Infinite Assignment and Transportation Games," Discussion Paper 2000-43, Tilburg University, Center for Economic Research.
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