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A core-allocation for a network restricted linear production game

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  • Ichiro Nishizaki
  • Tomohiro Hayashida
  • Yuki Shintomi

Abstract

This paper deals with a linear production game with restricted communication. Based on the Owen solution (Owen in Math Progr 9:358–370, 1975 ), we propose a core-allocation reflecting the communication situation defined by a network. The core of a linear production game with unrestricted communication is included by that of the corresponding network restricted game. Taking this property into account, we develop a procedure for modifying the Owen solution to reflect the configuration of the enlarged core. Copyright Springer Science+Business Media New York 2016

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  • Ichiro Nishizaki & Tomohiro Hayashida & Yuki Shintomi, 2016. "A core-allocation for a network restricted linear production game," Annals of Operations Research, Springer, vol. 238(1), pages 389-410, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:389-410:10.1007/s10479-016-2109-4
    DOI: 10.1007/s10479-016-2109-4
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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    3. Nimrod Megiddo, 1978. "Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 189-196, August.
    4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    6. Francisco Fernández & MarÍa Fiestras-Janeiro & Ignacio GarcÍa-Jurado & Justo Puerto, 2005. "Competition and Cooperation in Non-Centralized Linear Production Games," Annals of Operations Research, Springer, vol. 137(1), pages 91-100, July.
    7. Jeroen Suijs & Peter Borm & Herbert Hamers & Marieke Quant & Maurice Koster, 2005. "Communication and Cooperation in Public Network Situations," Annals of Operations Research, Springer, vol. 137(1), pages 117-140, July.
    8. Ehud Kalai & Eitan Zemel, 1982. "Generalized Network Problems Yielding Totally Balanced Games," Operations Research, INFORMS, vol. 30(5), pages 998-1008, October.
    9. van Gellekom, J. R. G. & Potters, J. A. M. & Reijnierse, J. H. & Engel, M. C. & Tijs, S. H., 2000. "Characterization of the Owen Set of Linear Production Processes," Games and Economic Behavior, Elsevier, vol. 32(1), pages 139-156, July.
    10. Peleg, Bezalel, 1992. "Axiomatizations of the core," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 13, pages 397-412, Elsevier.
    11. Ehud Kalai & Eitan Zemel, 1982. "Totally Balanced Games and Games of Flow," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 476-478, August.
    12. Dov Samet & Eitan Zemel, 1984. "On the Core and Dual Set of Linear Programming Games," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 309-316, May.
    13. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    14. Takumi Kongo, 2010. "Difference between the position value and the Myerson value is due to the existence of coalition structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 669-675, October.
    15. Nishizaki, Ichiro & Sakawa, Masatoshi, 2001. "On computational methods for solutions of multiobjective linear production programming games," European Journal of Operational Research, Elsevier, vol. 129(2), pages 386-413, March.
    16. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
    17. Tijs, S.H. & van Gellekom, J.R.G. & Potters, J.A.M. & Reijnierse, J.H. & Engel, M.C., 2000. "Characterization of the Owen set of linear production processes," Other publications TiSEM bdf0c618-e9f1-496a-b977-0, Tilburg University, School of Economics and Management.
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