Computational results for games with coupled constraints

Abstract

This chapter provides some results for Nash games with coupled constraints, i.e., coupled action sets. Work on games with coupled action spaces has been going on for more than 50 years. These are also called generalized Nash games, games with coupled constraints, or social equilibria. Game theoretical formulations of problems and computational approaches towards solving coupled or generalized Nash games have been areas of much recent interest. We present some new results mainly based on the Lagrangian approach extension proposed in Pavel (Automatica 43(2):226–237, 2007). We review a relaxation via an augmented optimization, the Lagrangian extension in a game setup, followed by duality and hierarchical decomposition in a game setup.