Existence & uniqueness of consistent conjectural variation equilibrium in electricity markets

The real electricity markets are usually oligopoly, where market suppliers (generators) will have some market power and can adopt strategic bidding strategies for maximum profits. Generally, the game-theory based methods are the natural way to analyze the market equilibrium and study the strategic behaviors. As a widely studied method in game theory, the conjecture variation technique is reported to model the strategic behavior in deregulated electricity markets recently. Unfortunately, the conjecture variation models have been criticized for the drawback of logical inconsistence and abundant equilibria. Aim for this, the existence and uniqueness of consistent conjectural variation equilibrium in the electricity markets are investigated. Due to some good characteristics of electricity markets and using an infinite horizon optimization model, it is shown that the consistent conjecture variation will satisfy a coupled nonlinear equation system and there is only one equilibrium.