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Existence theorems for Nash equilibrium and equilibrium in secure strategies

Author

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  • Iskakov, M.

    (V. A. Trapeznikov Institute of Control Sciences RAS, Moscow)

Abstract

The paper proposes a method for constructing existence theorems for equilibrium in secure strategies (EinSS) on the basis of the well-known existence theorems for Nash equilibrium. The system of definitions of the EinSS is interpreted as the development of the logic of rational behavior in the defi nition of Nash equilibrium. It is proved that under the condition of "strong threats" for the existence of EinSS, it is sufficient to fulfill the conditions of the known existence theorem for the Nash equilibrium only on the sets of secure strategies. This statement is formulated both globally and locally, and is an effective tool for application to practical problems. It opens up the possibility of constructing various particular existence theorems for EinSS. As a demonstration of the proposed approach, from the Debreu's theorem of the existence of social equilibrium, the corresponding theorem of the existence of the EinSS is obtained.

Suggested Citation

  • Iskakov, M., 2022. "Existence theorems for Nash equilibrium and equilibrium in secure strategies," Journal of the New Economic Association, New Economic Association, vol. 56(4), pages 12-27.
    • Handle: RePEc:nea:journl:y:2022:i:56:p:12-27
    DOI: 10.31737/2221-2264-2022-56-4-1
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    equilibrium in secure strategies; Nash equilibrium; competitive deviations; noncompetitive deviations; Nash equilibrium existence theorems; rational choice theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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