Procedures for Computing Equilibria of the Oligopoly Expansion Game under Predetermined Multi-Period Pricings. Part 1 : Short-Run Optimal Spot Pricing

Long-run oligopolistic expansion behavior in an electricity supply market is modeled in the paper. The market is assumed to charge electricity prices equal to short-run marginal costs plus optimal rationing prices (optimal spot prices). Electricity generation firms can affect prices (and then affect their profit) only by their capacity. A two-stage game is used to model this market: first, firms independently and simultaneously invest their capacity; second, after these capacities are set up, firms sell electricity produced by them at optimal spot prices. An iterative procedure is formulated for computing equilibria of the game. In each cycle of the procedure, a set of three models, a Nasb-Cournot model, a short-run welfare optimization model and a short-run cost minimization model with fixed demand, are successively solved until a fixed point is obtained. It is shown that when the peak supply at all nodes are higher than the off-peak supply or the peak prices are upper bounded not higher than the Cournot prices, the fixed point of the procedure constitutes an equilibrium of the two-stage game. A minor modification of the procedure is used to model a long- run oligopoly where threat of entry exists. A market organized by three European countries is simulated by the procedure.