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Absolute optimal solution for a compact and convex game

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  • Nessah, Rabia
  • Tazdaı¨t, Tarik

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.

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  • 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.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:2:p:353-361
    DOI: 10.1016/j.ejor.2012.08.013
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    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. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    5. Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2023. "On The Strong Β-Hybrid Solution Of An N-Person Game," Post-Print hal-04204632, HAL.
    6. 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.

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