DOI: 10.1016/j.fss.2024.108879">
 

Necessary and sufficient conditions for the existence of fuzzy doubly strong equilibria in generalized fuzzy games

Document Type

Article

Publication Date

2024

Department/School

Mathematics

Publication Title

Fuzzy Sets and Systems

Abstract

The concept of doubly strong equilibrium is a refinement of the concept of strong Nash equilibrium which represents the most desirable situations for generalized games, where all players get the best among the available outcomes. In this paper, we use necessary and sufficient conditions for the existence of solutions of the Ky Fan minimax inequality to establish necessary and sufficient conditions for the existence of fuzzy doubly strong equilibria in generalized fuzzy games. As consequences, we obtain sufficient conditions for the existence of (fuzzy) strong Nash equilibria in generalized (fuzzy) games, including generalized games with countable infinitely many players, which generalize existing existence theorems for strong Nash equilibria in games.

Comments

J. Liu is a faculty member in EMU's Department of Mathematics and Statistics.

Link to Published Version

DOI: 10.1016/j.fss.2024.108879

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