Nash equilibrium problems with congestion costs and shared constraints

Abstract— Generalized Nash equilibria (GNE) represent extensions of the Nash solution concept when agents have shared strategy sets. This generalization is particularly relevant when agents compete in a networked setting. In this paper, we consider such a setting and focus on a congestion game in which agents contend with shared network constraints. We make two sets of contributions: (1) Under two types of congestion cost functions, we prove both existence and uniqueness of the primal generalized Nash equilibrium. The results are provided without a compactness assumption on the constraint set and are shown to hold when the mappings associated with the resulting variational inequality are non-monotone. Under certain assumptions, the local and global uniqueness of the primal-dual generalized Nash equilibrium is also proved. (2) We provide two distributed schemes for obtaining such equilibria: a dual and a primaldual algorithm. Convergence of both algorithms is analyzed and preliminary ...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Huibing Yin, Uday V. Shanbhag, Prashant G. Mehta
• Keywords: CDC 2009, Control Systems, Generalized Nash, Generalized Nash Equilibrium, Primal Generalized Nash