Calculating equilibria

Competition between oligopolist electricity generators is inhibited by transmission constraints. I present a supply function equilibrium (SFE) model of an electricity market with a single lossless, but constrained, transmission line. The market admits equilibria in which generator withhold energy in order to induce congestion, which further increases their local market power. Under appropriate assumptions on cost and demand functions, I obtain a planar autonomous system of ordinary differential equations for the SFE. Computational methods are developed to solve the system while respecting monotonicity constraints on the supply functions. Using these methods I can calculate SFE in network markets that range from fully isolated to fully integrated. I also find network markets for which the SFE is not unique.