Existence and uniqueness of consistent conjectural variation equilibrium in electricity markets

The game-theory based methods are widely applied to analyze the market equilibrium and to study the strategic behavior in the oligopolistic electricity markets. Recently, the conjecture variation approach, one of well-studied methods in game theory, is reported to model the strategic behavior in deregulated electricity markets. Unfortunately, the conjecture variation models have been criticized for the drawback of logical inconsistence and possibility of abundant equilibria. Aiming for this, this paper investigates the existence and uniqueness of consistent conjectural variation equilibrium in electricity markets. With several good characteristics of the electricity market and with an infinite horizon optimization model, it is shown that the consistent conjecture variation will satisfy a set of coupled nonlinear equations and there will be only one equilibrium. This result can provide the fundamentals for further applications of the conjecture variation approach.