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On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions

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  • Fu, Haifeng

Abstract

We show that each mixed strategy of a normal-form game can be reformulated as a pure strategy of an induced Bayesian game. Moreover, a normal-form game has a Pareto undominated mixed-strategy Nash equilibrium if and only if its induced Bayesian game has a pure-strategy Bayesian Nash equilibrium. By relying on the existence result of Pareto undominated pure-strategy Nash equilibrium in Bayesian games in Fu and Yu (2015), we also show that every normal-form game has a Pareto undominated mixed-strategy Nash equilibrium.

Suggested Citation

  • Fu, Haifeng, 2021. "On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions," Economics Letters, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:ecolet:v:201:y:2021:i:c:s0165176521000483
    DOI: 10.1016/j.econlet.2021.109771
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    References listed on IDEAS

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    1. Le Breton, Michel & Weber, Shlomo, 1997. "On existence of undominated pure strategy Nash equilibria in anonymous nonatomic games," Economics Letters, Elsevier, vol. 56(2), pages 171-175, October.
    2. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    3. Fu, Haifeng & Yu, Haomiao, 2018. "Pareto refinements of pure-strategy equilibria in games with public and private information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 18-26.
    4. Roy Radner & Robert W. Rosenthal, 1982. "Private Information and Pure-Strategy Equilibria," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 401-409, August.
    5. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    6. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
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