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A.V. Arutyunov, S.E. Zhukovskiy, Necessary condition of weak Nash equilibrium

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DOI: 10.23952/jano.8.2026.1.06
Volume 8, Issue 1, 1 April 2026, Pages 107-114

 

Abstract. We study a N-person game in normal form. We introduce the concept of weak Nash equilibrium. Unlike the Nash equilibrium, a weak equilibrium always exists if only the strategy sets are compact and the loss functions are continuous. Under the assumption that the sets of pure strategies are defined by equality constraints, necessary conditions of the weak Nash equilibrium are obtained. The necessary conditions obtained remain informative even in the case when the first derivative of the mappings defining the constraints degenerates at the point of weak equilibrium.

 

How to Cite this Article:
A.V. Arutyunov, S.E. Zhukovskiy, Necessary condition of weak Nash equilibrium, J. Appl. Numer. Optim. 8 (2026), 107-114.