Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.9.2025.2.07

Volume 9, Issue 2, 1 April 2025, Pages 283-295

 

Abstract. In the realm of two-person nonzero-sum games, several game-theoretic solution concepts, including saddle point, minimax value, and maximin value, all converge to a single and renowned solution: the Nash equilibrium point. Minimax problems enjoy widespread applications in game theory. However, existing literature primarily addresses payoff mappings in the context of real-valued or vector-valued functions, with limited exploration of set-valued mappings, especially in the case of two such mappings. In this paper, we embark on a comprehensive exploration and expansion of minimax techniques within the domain of game theory. Furthermore, we pave the way for a novel avenue of inquiry by delving into the realm of set-valued mappings, pushing the boundaries of game theory research. Our study also delves into the nuanced structure of saddle points, encompassing various types, including the (weak) loose semisaddle points. To illuminate these concepts, we provide illustrative example, shedding light on their practical implications and relevance in game theory.

 

How to Cite this Article:
Y.C. Lin, Interpretative analysis on loose semisaddle points for two-person game, J. Nonlinear Var. Anal. 9 (2025), 283-295.