Distributed iterative regularization algorithms for monotone Nash games

In this paper, we consider the development of single-timescale schemes for the distributed computation of Nash equilibria. In general, equilibria associated with convex Nash games over continuous strategy sets are wholly captured by the solution set of a variational inequality. Our focus is on Nash games whose equilibrium conditions are given by monotone variational inequalities, a class referred to as monotone Nash games. Unless suitably strong assumptions (such as strong monotonicity) are imposed on the mapping corresponding to the variational inequality, distributed schemes for computing equilibria often require the solution of a sequence of regularized problems, each of which has a unique solution. Such schemes operate on two timescales and are generally harder to implement in online settings. Motivated by this shortcoming, this work focuses on the development of three single timescale iterative regularization schemes that require precisely one projection step at every iteration. T...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Aswin Kannan, Uday V. Shanbhag
• Keywords: CDC 2010, Control Systems, Nash Games, Regularization Scheme, Variational Inequality