New insights on generalized Nash games with shared constraints: Constrained and variational equilibria

— We consider generalized noncooperative Nash games with “shared constraints” in which there is a common constraint that players’ strategies are required to satisfy. We address two shortcomings that the associated generalized Nash equilibrium (GNE) is known to have: (a) shared constraint games usually have a large number (often a manifold) of GNEs and (b) the GNE may not be the appropriate solution concept for exogenously imposed constraints. For (a), we seek a refinement of the GNE and study the variational equilibrium (VE), defined by [1], [2], as a candidate. It is shown that the VE and GNE are equivalent in a certain degree theoretic sense. For a class of games the VE is shown to be a refinement of the GNE and under certain conditions the VE and GNE are observed to coincide. To address (b), a new concept called the constrained Nash equilibrium (CNE) is introduced. The CNE is an equilibrium of the game without the shared constraint that is feasible with respect to this co...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Ankur A. Kulkarni, Uday V. Shanbhag
• Keywords: CDC 2009, Control Systems, Generalized Nash Equilibrium, Nash Equilibrium, Shared Constraint