Using equilibrium programs with equilibrium constraints to Model Bilevel Games in Restructured Electricity Markets with Locational Prices

We study a bilevel noncooperative game-theoretic model of restructured electricity markets, with locational marginal prices. Each player in this game faces a bilevel optimization problem that we model as a mathematical program with equilibrium constraints. The corresponding game is an example of an equilibrium program with equilibrium constraints. We establish sufficient conditions for the existence of pure-strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e., congestion, on the existence of equilibria. Then we study, for more general equilibrium programs with equilibrium constraints, the weaker pure-strategy concepts of local Nash and Nash stationary equilibria. We pose the latter as solutions of complementarity problems and show their equivalence with the former in some cases. Finally, we present numerical examples of methods that attempt to find local Nash equilibria or Nash stationary points of randomly generated electricity market games.