Single timescale regularized stochastic approximation schemes for monotone Nash games under uncertainty

Abstract-- In this paper, we consider the distributed computation of equilibria arising in monotone stochastic Nash games over continuous strategy sets. Such games arise in settings when the gradient map of the player objectives is a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation schemes. However, such techniques are characterized by a key shortcoming: they can accommodate strongly monotone mappings only. In fact, standard extensions of stochastic approximation schemes for merely monotone mappings require the solution of a sequence of related strongly monotone problems, a natively two-timescale scheme. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We first show that, under suitable assumptions, standard projection schemes can...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Jayash Koshal, Angelia Nedic, Uday V. Shanbhag
• Keywords: CDC 2010, Control Systems, Monotone Stochastic Nash, Stochastic Approximation Schemes, Strong Monotonicity