Transmission constraints and market concentration may prevent power markets from being fully competitive, allowing firms to exercise market power and raise prices above marginal cost. We present a strategic gaming model for analyzing such markets; it represents an oligopolistic market economy consisting of several dominant firms in an electric power network. Each generating firm submits bids to an ISO, choosing its bids to maximize profits subject to anticipated reactions by rival firms. The single-firm model is formulated as a Mathematical Program with Equilibrium Constraints (MPEC) with a parameter-dependent spatial price equilibrium problem as the inner problem. Power flows and pricing strategies are constrained by the ISO's linearized DC optimal power flow (OPF) model. A penalty interior point algorithm is used to compute a local optimal solution of the MPEC. Numerical examples based on a 30 bus network are presented, including multi-firm Nash equilibria in which each player solves an MPEC of the single-firm type.

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This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf (1994).Economics, Equilibrium Pricing; MIP models of markets, MIP Applications

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Conjectured supply function (CSF) models of competition among power generators on a linearized dc network are presented. As a detailed survey of the power market modeling literature shows, CSF models differ from previous approaches in that they represent each of GenCo's conjectures regarding how rival firms will adjust sales in response to price changes. The CSF approach is a more realistic and flexible framework for modeling imperfect competition than other models for three reasons. First, the models include as a special case the Cournot conjecture that rivals will not change production if prices change; thus, the CSF framework is more general. Second, Cournot models cannot be used when price elasticity of demand is zero, but the proposed models can. Third, unlike supply function equilibrium models, CSF equilibria can be calculated for large transmission networks. Existence and uniqueness properties for prices and profits are reported. An application shows how transmission limits and strategic interactions affect equilibrium prices under forced divestment of generation.This section provides a review of alternative approaches to modeling GenCo interactions in oligopolistic power markets. We include overviews of: equilibrium modeling approaches; representations of GenCo strategic interactions and their application; and complementarity models using dc networks. A. Use of Equilibrium Models for Power MarketsMost models of generator competition are based upon a general approach of defining a market equilibrium as a set of prices, producer input and output decisions, transmission flows, and consumption that simultaneously satisfy each market participant's first-order conditions for maximization of their net benefits [Karush-Kuhn-Tucker (KKT) conditions] while clearing the market (supply demand). The complete set of 0885-8950/02$17.00