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Pareto-optimal Nash equilibrium: Sufficient conditions and existence in mixed strategies

  • Mathematical Game Theory and Applications
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Abstract

This paper considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the non-cooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto optimal Nash equilibria in mixed strategies is proved.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. I. Zhukovskiy

  2. South Ural State University, Chelyabinsk, Russia

    K. N. Kudryavtsev

Authors
  1. V. I. Zhukovskiy
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  2. K. N. Kudryavtsev
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Correspondence to V. I. Zhukovskiy.

Additional information

Original Russian Text © V.I. Zhukovskiy, K.N. Kudryavtsev, 2015, published in Matematicheskaya Teoriya Igr i Ee Priloszheniya, 2015, No. 1, pp. 74–91.

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Zhukovskiy, V.I., Kudryavtsev, K.N. Pareto-optimal Nash equilibrium: Sufficient conditions and existence in mixed strategies. Autom Remote Control 77, 1500–1510 (2016). https://doi.org/10.1134/S0005117916080154

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