Existence, uniqueness, stability of linear supply function equilibrium in electricity markets

In this paper, an explicit mathematic proof is presented on the existence and uniqueness of non-cooperative equilibrium with linear supply functions in electricity markets. A rational adjustment model is proposed for the adjustment dynamics, which can be used to calculate the equilibrium efficiently. Based on the dynamic adjustment model, the equilibrium stability is studied. Some intuitive discussions are given such as how players in the market can find the equilibrium through learning based on the market information. Numerical test results support the analytical conclusions very well.