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Convex and Exact Games with Non-transferable Utility

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  • Csóka, P.

    (Microeconomics & Public Economics)

  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Kóczy, L.Á.

    (Microeconomics & Public Economics)

  • Pintér, M.

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 ∏-balanced, totally ∏-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex

Suggested Citation

  • Csóka, P. & Herings, P.J.J. & Kóczy, L.Á. & Pintér, M., 2009. "Convex and Exact Games with Non-transferable Utility," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2009031
    DOI: 10.26481/umamet/2009031
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    as
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    Cited by:

    1. 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.
    2. 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.
    3. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Pintér, Miklós, 2016. "A cardinal convex game with empty core," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 9-10.
    9. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    10. repec:spr:compst:v:74:y:2011:i:1:p:41-52 is not listed on IDEAS
    11. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    12. 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.
    13. 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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