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Semi-Infinite Assignment Problems and Related Games


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  • Llorca, N.
  • Tijs, S.H.
  • Timmer, J.B.

    (Tilburg University, Center for Economic Research)

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    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 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 Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-74.

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

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    Keywords: Infinite programs; assignment; cooperative games; balancedness;

    This paper has been announced in the following NEP Reports:


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    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.
    2. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
    3. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    4. 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.
    5. 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.
    6. 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.
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    Cited by:
    1. 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.
    2. 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.


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