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Absolute optimal solution for a compact and convex game

Author

Listed:
  • Rabia Nessah

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • Tarik Tazdaït

    (CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper investigates the existence of absolute optimal solutions for a partition P in continuous and quasiconcave games. We show that the P-consistency property introduced in the paper, together with the quasiconcavity and continuity of payoffs, permits the existence of P-absolute optimal solutions in games with compact and convex strategy spaces. The P-consistency property is a general condition that cannot be dispensed with for the existence of P-absolute optimal solutions. We also characterize the existence of P-absolute optimal solutions by providing necessary and sufficient conditions. Moreover, we suggest an algorithm for efficiently computing P-absolute optimal solutions.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Rabia Nessah & Tarik Tazdaït, 2013. "Absolute optimal solution for a compact and convex game," Post-Print hal-00785033, HAL.
    • Handle: RePEc:hal:journl:hal-00785033
    DOI: 10.1016/j.ejor.2012.08.013
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    References listed on IDEAS

    as
    1. Goh, C. J. & Yang, X. Q., 1999. "Vector equilibrium problem and vector optimization," European Journal of Operational Research, Elsevier, vol. 116(3), pages 615-628, August.
    2. Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
    3. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    4. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2009. "An interdisciplinary approach to coalition formation," European Journal of Operational Research, Elsevier, vol. 195(2), pages 487-496, June.
    5. Licun Xue, 2000. "Negotiation-proof Nash equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 339-357.
    6. repec:cor:louvrp:-987 is not listed on IDEAS
    7. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    8. 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.
    9. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    10. 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).
    11. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    12. Vidal-Puga, Juan J., 2008. "Forming coalitions and the Shapley NTU value," European Journal of Operational Research, Elsevier, vol. 190(3), pages 659-671, November.
    13. Nagarajan, Mahesh & Sosic, Greys, 2008. "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 719-745, June.
    14. Zhao, Jingang, 1999. "A [beta]-Core Existence Result and Its Application to Oligopoly Markets," Games and Economic Behavior, Elsevier, vol. 27(1), pages 153-168, April.
    15. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
    16. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, 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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    Citations

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    Cited by:

    1. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2017. "Existence and computation of Berge equilibrium and of two refinements," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 7-15.
    2. 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.
    3. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2023. "On the strong $$\beta$$ β -hybrid solution of an N-person game," Theory and Decision, Springer, vol. 94(3), pages 363-377, April.
    4. 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.
    5. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    6. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2023. "On The Strong Β-Hybrid Solution Of An N-Person Game," Post-Print hal-04204632, HAL.

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