Nash equilibrium design and coordination in hierarchical systems

This paper deals with the problem of Nash equilibrium design in noncooperative games in which agents anticipate values of Lagrange multipliers (prices) coordinating their payoffs. Sufficient conditions are formulated for Nash-implementation of regular and isolated solution to conditional optimization problem with equality constraints. Nash equilibrium design procedure for price-anticipation game is proposed as well. The problem is studied within the framework of control and coordination theory for hierarchical systems. A network congestion control game is discussed as a motivating example.