Estimation, Learning, and Stability Analysis of Supply Function Equilibrium Game for Generation Companies

In this paper, the competition among supplier agents in a uniform price electricity market is modeled as a supply function equilibrium game, where the players decide on a function of price versus quantity. The game problem is studied in two cases: in the first one, the players determine the intercept of the linear supply function; and in the second one, they choose its slope. It is assumed that the players do not have access to the cost function of the rivals and also cannot observe the current decision of them. Therefore, they estimate the future decisions of the rivals using their historical information. A nonlinear dynamic gradient learning method, namely myopic adjustment, is proposed for decision making of the players which works together with the estimation method. In each case, the Nash equilibrium point is analyzed and is shown that is a projection, onto a suitable subspace, of an equilibrium point of the dynamical system. Sufficient conditions for the stability of such equilibrium point of the proposed estimation and learning dynamics is obtained and an estimation of the corresponding region of attraction is computed using Lyapunov's second method.