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Equilibrium existence in games: Slight single deviation property and Ky Fan minimax inequality

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  • Scalzo, Vincenzo

Abstract

In this paper, we exhibit a relation between the Nash equilibrium existence problem in ordinal games and the Ky Fan minimax inequality. In this way, we obtain new sufficient conditions for the existence of equilibria. The main tools used in the paper are a necessary condition introduced in Nassah and Tian (2016) for normal form games and a generalization of the single deviation property. Examples compare our result with the previous ones.

Suggested Citation

  • Scalzo, Vincenzo, 2019. "Equilibrium existence in games: Slight single deviation property and Ky Fan minimax inequality," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 197-201.
    • Handle: RePEc:eee:mateco:v:82:y:2019:i:c:p:197-201
    DOI: 10.1016/j.jmateco.2019.02.008
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    Cited by:

    1. Scalzo, Vincenzo, 2023. "Existence and stability results on the unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 1-9.
    2. Blas Pelegrín & Pascual Fernández & María Dolores García, 2023. "On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand," Networks and Spatial Economics, Springer, vol. 23(4), pages 825-843, December.
    3. Khan, M. Ali & McLean, Richard P. & Uyanik, Metin, 2024. "On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    4. Tieying Huang & Jiuqiang Liu, 2022. "Fuzzy Strong Nash Equilibria in Generalized Fuzzy Games with Application in Urban Public-Sports Services," Mathematics, MDPI, vol. 10(20), pages 1-10, October.
    5. Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.

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