A high price yielding very high profits may lead to the entry of firms into the industry; thereby make the Chamberlin solution impossibility. Firm 1 is the Stackelberg leader, and firm 2 is the follower; besides, we denote the output of firm at time period by , which is updated according to discrete time steps. Thus there is market equilibrium if their desires are consistent to each other. The main purpose of this section is to show the qualitative behavior of a Stackelberg–Cournot duopoly game with heterogeneous players, described by the system (13), and exhibit how the system evolves when the model parameters take different level of values. Referring to previous literatures, naïve [5–9], boundedly rational [3, 6–8, 10–15], adaptive [6, 7, 9, 10, 13, 16], local monopolistic approximation [15, 17–19], expectations are commonly available strategies and have been adopted to describe dynamics in Cournot games [6–8, 18, 20–22] and Stackelberg games [3, 15, 23, 24], with two or more players. We consider a duopoly Stackelberg–Cournot game where two firms, labelled by , produce perfect substitute goods with production levels , respectively, and sell them at discrete time periods on a common market. In this situation, it tries to adjust its price and output. They are based on the assumption that the value of the rival’s variable is given regardless of the seller’s own moves. In this rival’s price increases. There are different diagrams that you can use to explain 0ligopoly markets. The models are: 1. Each seller determines the maximum profits he can get both by being a leader and a follower. How to draw a duopoly equilibrium summary diagram - YouTube An oligopolistic market has a structure where there are a tiny number of firms producing the same or homogeneous commodities, which are sold in a common market. The Stackelberg Model. Accordingly, assuming that В will continue to sell the same quantity AB (=BD1), it regards the remaining portion of the market OB available to it. Because the simulation graph in the paper is based on the virtual data under certain conditions, the data used to support the findings of this study are available from the corresponding author upon request. (4), e.g., the dynamical equation of firm 2 has the form as follows: We combine equations (11) and (12); therefore, the two-dimensional system that characterizes the dynamics of a Stackelberg–Cournot duopoly game with heterogeneous players is given by. Our paper differs from these aforementioned references in three ways. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. The equilibrium is again stable and determinate. This is illustrated in the following figures where the leadership point LA of seller A is shown to lie on the reaction curve of firm B, and the leadership point LB of seller В is shown to lie on the reaction curve of firm A. The exclusion of the problem of collusion has led to unrealistic results. Due to enterprises’ bounded rationality and the universality of R&D spillovers, we need to consider the following questions: (i) in a perfectly rational duopoly market consisting of two stages of successive R&D and simultaneous production, what is the relationship between equilibrium output and R&D input? The model is silent about the period within which one firm reacts and adjusts its output to the moves of the other. The Stackelberg model is a quantity leadership model. The Cournot model can be extended even to more than two firms. In this paper, a duopoly Stackelberg model of competition on output with stochastic perturbations is proposed. A. Amer, “Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation,”, X. S. Luo, G. Chen, B. Hong Wang, and J. Qing Fang, “Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems,”.
2020 stackelberg duopoly model diagram