Supply function equilibrium game with myopic adjustment and adaptive expectation

In this paper, the competition among supplier agents in an auction is modeled as a supply function equilibrium game. The strategy of each player is a function of price versus quantity. Each player wants to maximize a monetary payoff over the time-steps in a repeated game. It is assumed that the players have only access to the historical information of the rivals´ decisions. Therefore, the players need to estimate the decision of the rivals for the next step. A nonlinear dynamic gradient learning method, namely myopic adjustment, is proposed for decision making of the players which works together with an adaptive expectation method. It is shown that the game model admits a unique Nash equilibrium point. A sufficient condition for the convergence of the proposed method to the Nash equilibrium point is also derived and a region attraction of the proposed dynamical system is computed using Lyapunov´s second method.