The generalized Nash game proposed by Rosen

TL;DR

This paper analyzes Rosen's generalized Nash game, reducing it to classical game theory, and establishes conditions for equilibria and existence results using variational inequalities, extending to non-compact cases.

Contribution

It provides a reduction of Rosen's generalized Nash game to classical game theory and derives new equilibrium conditions and existence results under broader conditions.

Findings

Rosen's game can be reduced to a classical game.

Necessary and sufficient conditions for generalized Nash equilibria are established.

Existence of equilibria is proved under coerciveness in non-compact cases.

Abstract

We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be deduced from the one given by Arrow and Debreu. We also establish necessary and sufficient conditions for a point to be a generalized Nash equilibrium employing the variational inequality approach. Finally, some existence results are given in the non-compact case under coerciveness conditions.