# stackelberg model of duopoly

Cournot Competition describes an industry structure (i.e. The Stackelberg price competition model is an important model that captures the game theory behavior of a market where one company has a dominant position. There are two primary types of duopolies: the Cournot Duopoly (named after Antoine Cournot) and the Bertrand Duopoly (named after Joseph Bertrand). Bertrand’s Duopoly Model: Cournot assumes that the duopolist takes his rivals’ sales as constant … If the competitive firms engage in such behavior, they will hurt themselves. That is, start analyzing the decision of the follower. Each firm’s quantity demanded is a function of not only the price it charges but also the price charged […] QS: total Stackelberg output It was developed in 1934 by Heinrich Stackelberg in his “Market Structure and Equilibrium” and represented a breaking point in the study of market structure, particularly the analysis of duopolies since it was a model based on different starting … It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. The other companies then take this price as given and set the own output. In the Stackelberg model, we have a single firm that has a significantly large market share. The dominant firm’s demand curve should be used to determine the price at which the dominant firm will sell its product. is a sequential model, which means that the dominant firm first sets the price, which is then used by the other firms to determine their optimal production. The large market share can be assumed to be the result of greater scale and thus lower costs. In the Stackelberg duopoly the leader (Stackelberg firm) moves first and the follower moves second. Topic 4: Duopoly: Cournot-Nash Equilibrium. We now turn to the situation when there are a small number of firms in the industry and these firms have the option of colluding with or competing with each other. Nevertheless, the loss is lower in the Stackelberg duopoly than in Cournot’s. The Stackelberg model is based on the third case of a Stackelberg duopoly. MC: marginal cost. A price decrease by one of the smaller competitive firms will lead to a drop in the price by the dominant firm. An extensive-form representation is often used to analyze the Stackelberg leader-follower model. Thus, the competitive firms have no incentive to lower the price. This is different from the Cournot duopoly, where both companies set their production simultaneously. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. The total quantity supplied by all firms then determines the market price. (iv) Modern Game Theory Model. In the context of entry, firm 1 is the established firm, and firm 2 the prospective entrant. – A duopoly is an oligopoly with only two firms. In particular, the dominant firm will set the price such that marginal cost (MC) equals marginal revenue (MR). Therefore, each company has t… One of these companies is known as a leading company , it already has a dominant position and because it has a large number of strategies that determine the one of its followers or its competitors. 2. . In Section 3, the existence and stability of equilibrium points in the dynamical system are analyzed, and the stable regions are also calculated. Cournot model introduced by French Economist Augustin Cournot in 1838. While the Stackelberg model was originally formulated as a duopoly model, nowadays it is often discussed as a model with one dominant firms and a large number of smaller firms. Cournot competition is an economic model in which competing firms choose a quantity to produce independently and simultaneously, named after … Total production will be greater and prices lower, but player one will be better off than player two, which serves to highlight two things: the importance of accurate market information when defining a strategy, and the interdependence of each player’s strategies, especially when there is a market leader (with the benefit of moving first) and a follower. 2.2 The Model. Under this Cournot Duopoly model, it is assumed that the players would make an arrangement to divide the market into half and then share it. It is important to note that the dominant firm believes that the quantity supplied by the other smaller companies decreases when the price goes down. The reaction as a function of q1 (blue lines) is as follows: Firm 1 (leader) anticipates the follower’s behavior and takes it into consideration to make the strategic choice of q1: Therefore, the quantities sold by each firm at equilibrium are: The perfect equilibrium of the game is the Stackelberg equilibrium. In a dynamic context (repeated games), the models need to be reconsidered. Emphasis is laid on the number of goods that are produced indicating that this is what would shape the competition between the 2 firms. In this paper, a duopoly Stackelberg model of competition on output with stochastic perturbations is proposed. This model applies where: (a) the firms sell homogeneous products, (b) competition is based on output, and (c) firms choose their output sequentially and not simultaneously. In this game, the leader has decided not to behave as in the Cournot’s model, however, we cannot ensure that the leader is going to produce more and make more profits than the follower (production will be larger for the firm with lower marginal costs). This price decrease will then lead the smaller firms to decrease output or exit the industry. For firm 2 (follower), the problem is similar to the Cournot’ model. (ii) Hotellings Spatial Equilibrium Model. In simple words, let us assume a … If the competitive firms engage in such behavior, they will hurt themselves. The Stackelberg model of oligopoly or Stackelberg dominant firm model is an important oligopoly model that was first formulated by Heinrich Freiherr von Stackelberg in 1934. It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. PPC: perfect competition price STACKELBERG DUOPOLY MODEL Strategic Game Developed by German Economist Heinrich Von Stackelberg in 1934 Extension of Curnot model There are two firms, which sell homogenous products It is a sequential game not simultaneous 4. We discussed that this company tends to set the price based on its marginal cost. Stackelberg duopoly. A duopoly is a form of oligopoly, where only two companies dominate the market. The number of firms is restricted to … The principal diﬁerence between the Cournot model and the Stack- elberg model is that instead of moving simultaneously (as in the Cournot model) the ﬂrms now move sequentially. Thus, the dominant firm’s demand for its product is related to the market demand curve in the way shown in the below figure. They accumulate capacity through costly investment, with capital accumulation dynamics being affected by an additive shock the mean and variance of which are known. Stackelberg Model of Duopoly Stackelberg Duopoly Suppose that two rms (Firm 1 and Firm 2) face an industry demand P = 150 Q where Q = q 1 + q 2 is the total industry output. According to the law of supply and demand, a high level of output results in a relatively low price, whereas a lower level of output results in a relatively higher price. Finally, some remarks are presented in Section 6. This is different from the Cournot duopoly, where both companies set their production simultaneously. C) one firm makes its output decision before the other. There are two firms, which sell homogeneous products, and are subject to the same demand and cost functions. In game theory, a Stackelberg duopoly is a sequential game (not simultaneous as in Cournot’s model). It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. • Compared to perfect competition – Firms face downward sloping demand and thus can choose their price. Why doesn't the first-mover announce that its production is Q1 = 30 in order to exclude the second firm from the market (i.e., Q2 = … -Stackelberg’s model is a sequential game, Cournot’s is a simultaneous game; -In Stackelberg duopolies, the quantity sold by the leader is greater than the quantity sold by the follower, while in Cournot duopolies quantity is the same for both firms; -When comparing each firm’s output and prices, we have: -With regard to total output and prices we have the following: QC: total Cournot output The Cournot and Stackelberg duopoly theories in managerial economics focus on firms competing through the quantity of output they produce. Stackelberg Model of Duopoly Stackelberg’s Model of Duopoly also has to do with companies trying to decide how much of a homogeneous good to produce. Lope Gallego. The quantities of the products are x1, x2; the prices, pi, P2. This level of output then determines the market price. In the Stackelberg model of duopoly, one firm serves as the industry leader. This is the price for which the market price equals their marginal cost. The Bertrand duopoly model examines price competition among firms that produce differentiated but highly substitutable products. Thus, if firm A makes its decision first, firm A is the industry leader and firm B reacts to or follows firm A’s decision. There are two firms, which sell homogeneous products, … The price in the market depends on the marginal cost of this. There is a competitive numeraire sector whose output is x0. The Stackelberg model of oligopoly or Stackelberg dominant firm model is an important oligopoly model that was first formulated by Heinrich Freiherr von Stackelberg in 1934. STACKELBERG DUOPOLY MODEL ATHIRA.T 1ST M.AECONOMICS GOVT.COLLEGEMALAPPURAM 3. To see this page as it is meant to appear, please enable your Javascript! The Stackelberg leadership model is a sequential model, which means that the dominant firm first sets the price, which is then used by the other firms to determine their optimal production. -. However, in making its decision, firm A must anticipate how firm B reacts to that decision. This video discusses about the Stackelberg Duopoly model in Hindi language. Both rms have the same unit production cost c = 30. is an important oligopoly model that was first formulated by Heinrich Freiherr von Stackelberg in 1934. One firm, the leader, is perhaps better known or has greater brand equity, and is therefore better placed to decide first which quantity q1 to sell, and the other firm, the follower, observes this and decides on its production quantity q2. Duopoly Models: There are four main duopoly models which explain the price and quantity determinations in duopoly. In the Stackelberg model, we have a single firm that has a significantly large market share. The Nash equilibrium is not Pareto efficient (isoprofit curves, green curves, are not tangent to each other) and therefore, there is a loss in economic efficiency. The classic Stackelberg game is divided into two stages. Since the Stackelberg duopoly game is the most typical and simplest dynamic model in classical oligopoly game theory, we focus on its quantum version here. The long-run impact of one the small firms price decrease will be an increase in the market share of the small firms as they are forced to exit the market. PM: monopoly price When it comes to economic efficiency, the result is similar to Cournot’s duopoly model. In a standard Stackelberg duopoly situation there are two firms in a market. The main findings are the following. It was formulated by Heinrich Von Stackelberg in 1934. The basic model * The simplest case I consider is of a quantity-setting duopoly. In particular, the dominant firm will set the price such that marginal cost (MC) equals marginal revenue (MR). Theories of the Term Structure of Interest Rates, Non-accelerating Inflation Rate of Unemployment, Capital Structure Irrelevance Proposition, Discount for Lack of Marketability (DLOM). We also consider endogenous roles by adopting the observable delay … In Section 5, we exerted control on the duopoly Stackelberg game model. Models of Oligopoly • An oligopolyis a market with only a few important sellers. B) all firms enter the market simultaneously. The Chamberlin Model: Prof. Chamberlin proposed a stable duopoly solution recognising mutual … Thus, the competitive firms have no incentive to lower the price. The Stackelberg model is more appropriate than the Cournot model in situations where A) there are more than two firms. We investigate Stackelberg mixed duopoly models where a state‐owned public firm and a foreign private firm compete. D) firms will be likely to collude PC: Cournot price The model 2.1. For simplicity here we consider as duopoly situation, as in Cournot’s model. The other firms will then maximize profits by using this price to set their own output. It describes the strategic behaviour of industries in which there is a dominant firm or a natural leader and the other firms are the followers. The duopoly Stackelberg model. See instructions, Present Value of Growth Opportunities (PVGO). QPC: total perfect competition output In Section 2, the nonlinear duopoly Stackelberg–Cournot model is described, and a two-dimensional discrete system with heterogeneous players is formulated. Assume that rst Firm 1 moves and chooses q 1:In the second stage, after observing q 1;Firm 2 moves and chooses q 2: Saltuk Ozerturk (SMU) Stackelberg The large market share can be assumed to be the result of greater scale and thus lower costs. To find the Nash equilibrium of the game we need to use backward induction, as in any sequential game. PS: Stackelberg price The Stackelberg leadership model is a model of a duopoly. The companies in a duopoly tend to compete against one another, reducing the … an oligopoly) in which competing companies simultaneously (and independently) chose a quantity to produce. Stackelberg Model: Stackelberg’s equilibrium is mainly based on Stackelberg’s theory of competition, which tells us that two or more companies compete in order to completely dominate the market. I propose a dynamic duopoly model where firms enter simultaneously but compete hierarchically á la Stackelberg at each instant over time. The price in the market depends on the marginal cost of this dominant firm. The long-run impact of one the small firms price decrease will be an increase in the market share of the small firms as they are forced to exit the market. by one of the smaller competitive firms will lead to a drop in the price by the dominant firm. QM: total monopoly output This price decrease will then lead the smaller firms to decrease output or exit the industry. In stage 1, theplanning phase, each player chooses strategies, and concludes forward contracts for output. Now that we know how decisions based on quantities affect the market equilibrium, let’s see what happens when we deal with prices, starting with the Bertrand duopoly. Stackelberg model is a leadership model that allows the firm dominant in the market to set its price first and subsequently, the follower firms optimize their production and price. The Stackelberg model is a quantity leadership model. Also referred to as a “decision tree”, the model shows the combination of outputs and payoffs both firms have in the Stackelberg game Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. To begin with, we assume that there are only two firms---a situation called duopoly. Stackelberg Model. 2. In game theory, a Stackelberg duopoly is a sequential game (not simultaneous as in Cournot’s model). Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. As the industry leader, the firm is able to implement its decision before its rivals. We examine a desirable role (either leader or follower) of the public firm. Sorry, you have Javascript Disabled! (iii) Stackelberg's Model. Iqbal and Toor first gave a quantum perspective on the Stackelberg duopoly game by using Marinatto-Weber quantum scheme presented in. While the Stackelberg model was originally formulated as a duopoly model, nowadays it is often discussed as a model with one dominant firms and a large number of smaller firms. In the Stackelberg model, suppose the first-mover has MR = 15 - Q1, the second firm has reaction function Q2 = 15 - Q1/2, and production occurs at zero marginal cost. This level of output then determines the market price. Stackelberg and Cournot equilibria are stable in a static model of just one period. It was developed in 1934 by Heinrich Stackelbelrg in his “Market Structure and Equilibrium” and represented a breaking point in the study of market structure, particularly the analysis of duopolies, since it was a model based on different starting assumptions and gave different conclusions to those of the Cournot’s and Bertrand’s duopoly models. 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