Multidimensional Evolution Effects on Non-Cooperative Strategic Games

In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in multidimensions. We also define an equivalent dynamic quasi-variational inequality problem. The existence of equilibria is established, and a spot electricity market problem is reformulated in terms of the proposed dynamic generalized Nash equilibrium problem. Employing the theory of projected dynamical systems, we illustrate our approach by applying it to a 39-bus network case, which is based on the New England system. Moreover, we illustrate a comparative study between multiple time scales and a single time scale by a simple numerical experiment.