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Convex and exact games with non-transferable utility

Author

Listed:
  • Csóka, Péter
  • Jean-Jacques Herings, P.
  • Kóczy, László Á.
  • Pintér, Miklós

Abstract

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of [Pi]-balanced, totally [Pi]-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

Suggested Citation

  • Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
  • Handle: RePEc:eee:ejores:v:209:y:2011:i:1:p:57-62
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    References listed on IDEAS

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    1. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    2. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650.
    3. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    4. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Discussion Paper 2000-108, Tilburg University, Center for Economic Research.
    5. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2009. "Stable allocations of risk," Games and Economic Behavior, Elsevier, vol. 67(1), pages 266-276, September.
    6. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    7. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    8. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    9. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    10. Granot, D & Maschler, M & Owen, G & Zhu, W.R., 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 219-244.
    11. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    12. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    13. Demange, Gabrielle, 1987. "Nonmanipulable Cores," Econometrica, Econometric Society, vol. 55(5), pages 1057-1074, September.
    14. Ichiishi,Tatsuro, 1993. "The Cooperative Nature of the Firm," Cambridge Books, Cambridge University Press, number 9780521414449.
    15. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    16. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    17. Peleg, Bezalel, 1986. "A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 83-87, February.
    18. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    19. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Cited by:

    1. Péter Csóka & P. Herings & László Kóczy, 2011. "Balancedness conditions for exact games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 41-52, August.
    2. repec:wsi:igtrxx:v:17:y:2015:i:04:n:s0219198915500085 is not listed on IDEAS
    3. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
    4. Bezalel Peleg & Peter Sudhölter, 2015. "On Bargaining Sets of Convex NTU Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-7.
    5. Pintér, Miklós, 2016. "A cardinal convex game with empty core," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 9-10.
    6. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    7. repec:spr:compst:v:74:y:2011:i:1:p:41-52 is not listed on IDEAS
    8. Keyzer, Michiel & van Wesenbeeck, Cornelia, 2011. "Optimal coalition formation and surplus distribution: Two sides of one coin," European Journal of Operational Research, Elsevier, vol. 215(3), pages 604-615, December.

    More about this item

    Keywords

    NTU games Exact games Convex games;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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