A method for analyzing Nash equilibrium based on clustering of generation companies

Feasibility of Nash equilibrium in generation markets is analyzed using a game theory for simplified competitive electricity markets. Generation companies in the markets are classified into two groups by the state of each company at equilibrium and a new method for obtaining Nash equilibrium in N-company spot markets is explored. Spot markets are assumed to be operated as uniform pricing auctions and generation companies are assumed to submit their bids into the auctions in the form of a seal-bid. The uniform pricing auctions in this analysis are formulated as games in which generation companies correspond to the players. The coefficient of the bidding function of company-n is assigned to the strategy of the player-n (company-n) and the payoff of the player-n is defined by his profit from the uniform price auction. Based on the concept of residual demand, best response functions of each generation company in the N-company auctions are analytically derived. Finally, an efficient way to obtain all the possible equilibrium set pairs and to examine their feasibilities as Nash equilibriums are suggested. A simple numerical example with three generation companies is demonstrated to show the basic ideas of the proposed method.