Abstract
The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.
Highlights
In the oligopolistic market, oligopoly firms compete in quantity or price
The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality
In this paper we have proposed a price Stackelberg duopoly game model with boundedly rational players
Summary
Oligopoly firms compete in quantity or price. We all know that Cournot model [1] is one of the most famous quantity game models, in which all firms (players) are provided with naive expectations. Some researchers have studied all sorts of triopoly quantity game models [8,9,10,11,12,13]. In Bertrand model, each firm will try to reduce its product price, until its products are selling at no profit. Boundedly rational duopoly and triopoly price game models with differentiated products have been studied in [16,17,18,19]. There is no result for boundedly rational price Stackelberg in a differentiated products market.
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