Generalized Ordinal Nash Games: Variational Approach

TL;DR

This paper introduces a variational approach to analyze the existence of solutions in generalized ordinal Nash games, where players' preferences are represented by binary relations without requiring utility functions.

Contribution

It presents a novel variational framework for studying generalized ordinal Nash games, extending solution existence analysis beyond utility-based preferences.

Findings

Provides conditions for the existence of solutions in generalized ordinal Nash games.

Extends variational inequality methods to non-utility-based preference relations.

Offers a new analytical tool for game theory with non-standard preferences.

Abstract

It is known that the generalized Nash equilibrium problem can be reformulated as a quasivariational inequality. Our aim in this work is to introduce a variational approach to study the existence of solutions for generalized ordinal Nash games, that is, generalized games where the player preferences are binary relations that do not necessarily admit a utility representation.