Fast learning methodologies for the Stackelberg and Cournot oligopoly models

We propose a learning process for a Stackelberg production model by which the leader predicts the follower’s response function and constructs a behavior leading to the maximization of his profit. When implementing the learning process, each player knows his costs, but not those of the competitor. At each step of the learning process, a game of Stackelberg is played and each player receives their payoff. The learning process continues until the leader is convinced of the correctness of his prediction. At this point, he reaches his maximum profit. We consider an example that applies the model to find rational leader behavior. Furthermore, we extend our analysis to a learning process in the context of an oligopoly game comprising three players. By applying the training process in line with the essence of the Stackelberg game, we achieve accelerated convergence to the equilibrium point in a Cournot game involving three players. Notably, the proposed learning process operates effectively under conditions of incomplete market information. Several illustrative examples underscore the application of the learning process in discerning the rational behavior of a leader in a two-player game and the rational behavior of players in a Cournot game involving three players.