Variational Analysis of Generalized Ordinal Nash Games on Banach Spaces

Shivani Valecha () and Asrifa Sultana ()
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Shivani Valecha: Indian Institute of Technology Bhilai
Asrifa Sultana: Indian Institute of Technology Bhilai

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 10, 25 pages

Abstract: Abstract We study the generalized ordinal Nash games defined over Banach spaces by employing variational techniques. To reformulate these games in terms of 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 to obtain an equilibrium for the proposed game by solving an auxiliary quasi-variational inequality. Based on this quasi-variational reformulation, we derive the existence of equilibrium for generalized ordinal Nash games with mid-point continuous preference maps. We apply the derived results to ensure the presence of Pareto equilibrium for multi-objective games and dynamic electricity markets.

Keywords: Quasi-variational inequality; Generalized ordinal Nash games; Dynamic electricity market; Binary relations; 49J53; 58E35; 65K10; 91A35 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02838-7

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