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Semi-infinite assignment problems and related games

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Author Info
Llorca, N.
Tijs, S.
Timmer, J. (Tilburg University, Center for Economic Research)
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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 74.

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Date of creation: 1999
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Handle: RePEc:dgr:kubcen:199974

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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.:
  1. 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. [Downloadable!] (restricted)
  2. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
  3. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation, Yale University. [Downloadable!]
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  4. Timmer, J. & Llorca, N. & Tijs, S., 1999. "Games arising from infinite production situations," Discussion Paper 57, Tilburg University, Center for Economic Research. [Downloadable!]
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  1. Sanchez-Soriano, J. & Llorca, N. & Tijs, S., 2000. "Semi-infinite assignment and transportation games," Discussion Paper 43, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Sanches-Soriano, J. & Llorca, N. & Tijs, S. & Timmer, J.B., 2000. "On the core of semi-infinite transportation games with divisible goods," Discussion Paper 89, Tilburg University, Center for Economic Research. [Downloadable!]
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