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Convex and exact games with non-transferable utility

Author

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  • 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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    2. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    3. 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.
    4. 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.
    5. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    6. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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    12. Pintér, Miklós, 2016. "A cardinal convex game with empty core," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 9-10.
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    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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