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Convex and Exact Games with Non-transferable Utility

Author

Listed:
  • Péter Csóka

    (Department of Finance, Corvinus University of Budapest)

  • P. Jean-Jacques Herings

    (Department of Economics, Maastricht University)

  • László Á. Kóczy

    (Keleti Faculty of Economics, Budapest Tech and Department of Economics, Maastricht University)

  • Miklós Pintér

    (Department of Mathematics, Corvinus University of Budapest)

Abstract

We generalize exactness to games with non-transferable utility (NTU). In an exact game 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 study 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

  • Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy & Miklós Pintér, 2009. "Convex and Exact Games with Non-transferable Utility," Working Paper Series 0904, Óbuda University, Keleti Faculty of Business and Management.
    • Handle: RePEc:pkk:wpaper:0904
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    References listed on IDEAS

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    Cited by:

    1. Junnosuke Shino & Shinichi Ishihara & Shimpei Yamauchi, 2022. "Shapley Mapping and Its Axiomatizations in n -Person Cooperative Interval Games," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    2. Elena Parilina & Stepan Akimochkin, 2021. "Cooperative Stochastic Games with Mean-Variance Preferences," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    3. 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.
    4. M. G. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. A. Mosquera, 2020. "On benefits of cooperation under strategic power," Annals of Operations Research, Springer, vol. 288(1), pages 285-306, May.
    5. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    6. 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.
    7. Jesús Getán & Josep Izquierdo & Jesús Montes & Carles Rafels, 2015. "The bargaining set for almost-convex games," Annals of Operations Research, Springer, vol. 225(1), pages 83-89, February.
    8. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    9. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    10. Pintér, Miklós, 2016. "A cardinal convex game with empty core," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 9-10.
    11. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    12. Berden, Caroline & Peters, Hans & Robles, Laura & Vermeulen, Dries, 2022. "Strategic transfers between cooperative games," Games and Economic Behavior, Elsevier, vol. 133(C), pages 77-84.
    13. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    14. 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.
    15. 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.

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    More about this item

    Keywords

    NTU Games; Exact Games; Convex Games;
    All these keywords.

    JEL classification:

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

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