Analyzing an optimistic attitude for the leader firm in duopoly models: A strong stackelberg equilibrium based on a lyapunov game theory approach

This paper presents a novel game theory approach for representing the Stackelberg dynamic duopoly models. The problem is fitted into a class of ergodic controllable finite Markov chains game. It is consider the case where a strong Stackelberg equilibrium point is convenient for both firms. We first analyze the best-reply dynamics of the Stackelberg duopoly model such that each firm’s best-reply strategies set agree with the set of maximizers of the opponents’ strategies. Then, the classical Stackelberg duopoly game is transformed into a potential game in terms of the Lyapunov theory. As a result, a duopoly model has the benefit that the best-reply dynamics results in a natural implementation of the behavior of a Lyapunov-like function. In addition, the strong equilibrium point properties of Stackelberg and Lyapunov meet in potential games. We validate the proposed method theoretically by computing the complexity and by a numerical experiment related to the duopoly model.