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Absolute Optimal Solution For a Compact and Convex Game

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  • Rabia Nessah

    (IESEG School of Management (LEM-CNRS))

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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Suggested Citation

  • Rabia Nessah, 2010. "Absolute Optimal Solution For a Compact and Convex Game," Working Papers 2010-ECO-07, IESEG School of Management.
    • Handle: RePEc:ies:wpaper:e201007
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    2. 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.
    3. 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.
    4. 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.
    5. Crettez, Bertrand & Nessah, Rabia, 2020. "On the existence of unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 41-47.
    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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