Variational Analysis of Generalized Games over Banach spaces

2024/07/26 by Asrifa Sultana, Sultana, Asrifa, Shivani Valecha +1
Computer Science · Economics, Econometrics and Finance · #49J40 #49J53 #91B06 #91B42 #FOS: Mathematics #Functional Analysis (math.FA) #Game Theory and Voting Systems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2407.18539

openalex publication_date 2024/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps.

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