LAUSR

Abstract This paper considers the problem of designing a Network such that a set of dynamic rules converges as fast as possible to the Nash equilibrium in a class of repeated games, despite the attempt of a jammer to slow down the convergence by cutting a certain number of edges. Particularly we consider a class of quadratic games, motivated by the demand response problem in electricity markets. For a given network structure, a set of dynamic rules, based on approximate gradient decent is described. The convergence speed depends on the graph through a matrix which in turn depends on the graph Laplacian. The network design problem is formulated as a zero sum game between a network designer aiming to improve the convergence speed and a jammer who tries to deteriorate it. Simple heuristics for the designer and the jammer problems are proposed and a numerical example is presented.