Using EPECs to model bilevel games in restructured electricity markets

Xinmin Hu (X.Huunsw.edu.au)
Daniel Ralph (d.ralphjbs.cam.ac.uk)

Abstract: 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 remodel as a mathematical program with equilibrium constraints, MPEC. The corresponding game is an example of an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for 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 existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We pose the latter as solutions of mixed complementarity problems, CPs, 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. The CP solver PATH is found to be rather effective in identifying Nash stationary points.

Keywords: electricity market, bilevel game, MPEC, EPEC, Nash stationary point, complementarity problem

Category 1: Complementarity and Variational Inequalities

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Citation: manuscript, Judge Business School, December 2005

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Entry Submitted: 01/05/2006
Entry Accepted: 01/05/2006
Entry Last Modified: 01/22/2006

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