Remarks on projected solutions for generalized Nash games

TL;DR

This paper investigates projected solutions in generalized Nash equilibrium problems, establishing new existence results without compactness assumptions and exploring their relationship with Nash equilibria.

Contribution

It introduces novel existence results for projected solutions in non-compact strategy sets and links these solutions to Nash equilibria in generalized games.

Findings

Projected solutions exist under broader conditions

Every projected solution relates to a Nash equilibrium in a different game

The relationship between projected solutions and Nash equilibria is clarified

Abstract

In this work, we focus on the concept of projected solutions for generalized Nash equilibrium problems. We present new existence results by considering sets of strategies that are not necessarily compact. The relationship between projected solutions and Nash equilibria is studied for the generalized Nash game proposed by Rosen. Finally, we demonstrate that every projected solution of a game is associated with a Nash equilibrium, but in a different game.