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Balanced games arising from infinite linear models

Author

Listed:
  • Vito Fragnelli
  • Fioravante Patrone
  • Enrico Sideri
  • Stef Tijs

Abstract

Kalai and Zemel introduced a class of flow-games showing that these games have a non-empty core and that a minimum cut corresponds to a core allocation. We consider flow-games with a finite number of players on a network with infinitely many arcs: assuming that the total sum of the capacities is finite, we show the existence of a maximum flow and we prove that this flow can be obtained as limit of approximating flows on finite subnetworks. Similar results on the existence of core allocations and core elements are given also for minimum spanning network models (see Granot and Huberman) and semi-infinite linear production models (following the approach of Owen). Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Vito Fragnelli & Fioravante Patrone & Enrico Sideri & Stef Tijs, 1999. "Balanced games arising from infinite linear models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 385-397, December.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:3:p:385-397
    DOI: 10.1007/s001860050077
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    Cited by:

    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. Timmer, J.B. & Llorca, N. & Tijs, S.H., 1999. "Games Arising from Infinite Production Situations," Other publications TiSEM 4573bb7e-7b84-4792-a330-b, Tilburg University, School of Economics and Management.
    3. Sánchez-Soriano, J. & Llorca, N. & Tijs, S.H. & Timmer, J.B., 2000. "On the Core of Semi-Infinite Transportation Games with Divisible Goods," Other publications TiSEM 469d59c1-b26f-402e-9cf0-e, Tilburg University, School of Economics and Management.
    4. Sanchez-Soriano, Joaquin & Llorca, Natividad & Tijs, Stef & Timmer, Judith, 2002. "On the core of semi-infinite transportation games with divisible goods," European Journal of Operational Research, Elsevier, vol. 142(3), pages 463-475, November.
    5. 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.
    6. Tijs, S.H. & Timmer, J.B. & Llorca, N. & Sánchez-Soriano, J., 2000. "The Owen Set and the Core of Semi-Infinite Linear Production Situations," Other publications TiSEM c28286c5-deeb-4e8a-b8dd-c, Tilburg University, School of Economics and Management.
    7. Tijs, S.H. & Timmer, J.B. & Llorca, N. & Sánchez-Soriano, J., 2000. "The Owen Set and the Core of Semi-Infinite Linear Production Situations," Discussion Paper 2000-49, Tilburg University, Center for Economic Research.
    8. J. Timmer & P. Borm & J. Suijs, 2000. "Linear Transformation of Products: Games and Economies," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 677-706, June.
    9. Hennet, Jean-Claude & Mahjoub, Sonia, 2010. "Toward the fair sharing of profit in a supply network formation," International Journal of Production Economics, Elsevier, vol. 127(1), pages 112-120, September.
    10. 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.
    11. Elisabeth Gutierrez & Natividad Llorca & Manuel Mosquera & Joaquin Sanchez-Soriano, 2019. "On horizontal cooperation in linear production processes with a supplier that controls a limited resource," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 169-196, October.
    12. Sánchez-Soriano, J. & Llorca, N. & Tijs, S.H. & Timmer, J.B., 2000. "Semi-Infinite Assignment and Transportation Games," Other publications TiSEM 87feb522-a153-45e6-b39d-f, Tilburg University, School of Economics and Management.
    13. Llorca, N. & Tijs, S.H. & Timmer, J.B., 1999. "Semi-Infinite Assignment Problems and Related Games," Discussion Paper 1999-74, Tilburg University, Center for Economic Research.
    14. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.

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