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The α-core in a multi-objective game with set payoffs

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  • Song, Qi-Qing
  • Guo, Min
  • Chi, Xin-Yi

Abstract

For the cooperative equilibria in α-core form, the balancedness and coalitionally C−security of games with usual utilities are extended to the games with discontinuous set payoffs. The existence of α−core for these games is established, which can deduce some typical results for normal form games. For continuous games, a quasi-concave-like set payoff is introduced. Based on the introduced set payoffs, the existence of α−core is also obtained. Examples are given to verify these results. Comparison with existing results in references shows that the introduced conditions are new to guarantee the existence of α−core for games with set payoffs.

Suggested Citation

  • Song, Qi-Qing & Guo, Min & Chi, Xin-Yi, 2024. "The α-core in a multi-objective game with set payoffs," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 32-39.
    • Handle: RePEc:eee:matsoc:v:131:y:2024:i:c:p:32-39
    DOI: 10.1016/j.mathsocsci.2024.07.001
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    References listed on IDEAS

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    1. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    2. Uyanık, Metin, 2015. "On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 213-231.
    3. Borm, P.E.M. & Tijs, S.H. & van den Aarssen, J.C.M., 1988. "Pareto equilibria in multiobjective games," Other publications TiSEM a02573c0-8c7e-409d-bc75-0, Tilburg University, School of Economics and Management.
    4. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    5. Crettez, Bertrand & Nessah, Rabia & Tazdaït, Tarik, 2022. "On the strong hybrid solution of an n-person game," Mathematical Social Sciences, Elsevier, vol. 117(C), pages 61-68.
    6. Jingang Zhao, 2018. "TU oligopoly games and industrial cooperation," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 14, pages 392-422, Edward Elgar Publishing.
    7. Paraskevas V. Lekeas, 2013. "Coalitional Beliefs In Cournot Oligopoly Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    8. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    9. Zhao, Jingang, 1991. "The Equilibria of a Multiple Object Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 171-182.
    10. repec:hal:journl:hal-04103610 is not listed on IDEAS
    11. L. S. Shapley & Fred D. Rigby, 1959. "Equilibrium points in games with vector payoffs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 6(1), pages 57-61, March.
    12. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    14. Zhao, Jingang, 2018. "Three little-known and yet still significant contributions of Lloyd Shapley," Games and Economic Behavior, Elsevier, vol. 108(C), pages 592-599.
    15. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    16. Bertrand Crettez & Naila Hayek, 2022. "A Dynamic Multi-Objective Duopoly Game with Environmentally Concerned Firms," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-26, March.
    17. Jingang Zhao, 1999. "The existence of TU -core in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 25-34.
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