Efficiency of linear supply function bidding in electricity markets

We study the efficiency loss caused by strategic bidding behavior from power generators in electricity markets. In the considered market, the demand of electricity is inelastic, the generators submit their supply functions (i.e., the amount of electricity willing to supply given a unit price) to bid for the supply of electricity, and a uniform price is set to clear the market. We aim to understand how the total generation cost increases under strategic bidding, compared to the minimum total cost. Existing literature has answers to this question without regard to the network structure of the market. However, in electricity markets, the underlying physical network (i.e., the electricity transmission network) determines how electricity flows through the network and thus influences the equilibrium outcome of the market. Taking into account the underlying network, we prove that there exists a unique equilibrium supply profile, and derive an upper bound on the efficiency loss of the equilibrium supply profile compared to the socially optimal one that minimizes the total cost. Our upper bound provides insights on how the network topology affects the efficiency loss.