The large market share can be assumed to be the result of greater scale and thus lower costs. (ii) When B is the leader and A the follower, the Stackelberg solution is . The model shows that a bargaining procedure and a collusive agreement becomes advantageous to both duopolists. The Stackelberg duopoly is a specific example, where the strategic positions of the players are not symmetric. In a dynamic context (repeated games), the models need to be reconsidered. We investigate Stackelberg mixed duopoly models where a state-owned public firm maximizing domestic social surplus, and a foreign firm compete. Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity s n ≥0 • Cost of producing s n: c n s n (1) Duo­polist A wants to be leader and B wants to be follower. We analyze two different scenarios: Stackelberg’s Duopoly Model (With Diagram) Article Shared by Trisha. We may now summarise Stackelberg’s model. This is point a (in figure 9.20) which lies on the lowest possible isoprofit curve of A, denoting the maximum profit A can achieve given B’s reaction curve. Firm B similarly, calculates its profits as a leader and as a follower: If B is the leader his profits are 918-75, If B acts as the follower his profits are 155-50. Thus, it is not obvious how the entanglement affects the equilibrium outcome prior to computing subgame perfect equilibria of the quantum game. Von Stackelberg’s model has interesting implications. In fact, the earliest duopoly model was developed in 1838 by the French economist Augustin Cournot. Stackelberg duopoly model definition. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. The two firms make simultaneous decisions. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival and incorporate it in his own profit function, which he then proceeds to maximise like a monopolist. Share Your Word File Each duopolist estimates the maximum profit that he would earn (a) if he acted as leader, (b) if he acted as follower, and chooses the behaviour which yields the largest maximum. The distinctive feature of the different oligopoly models is the way they attempt to capture the interdependence of firms in the market. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. Topic 4: Duopoly: Cournot-Nash Equilibrium. I had a conversation with a friend of mine yesterday about markets and I was trying to explain him some of the models. In summary, if only one firm is sophisticated, it will emerge as the leader, and a stable equilibrium will emerge, since the naive firm will act as a follower. Emphasis is laid on the number of goods that are produced indicating that this is what would shape the competition between the 2 firms. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. Welcome to EconomicsDiscussion.net! QS: total Stackelberg output QPC: total perfect competition output The Cournot and Stackelberg duopoly theories in managerial economics focus on firms competing through the quantity of output they produce. Stackelberg Model. MC: marginal cost. Share Your PPT File. 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. 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. Before publishing your Articles on this site, please read the following pages: 1. one for Bertrand, one for Stackelberg … 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 assumptions and gave different conclusions to those of the Cournot’s and Bertrand’s duopoly models. duopoly definition: 1. a situation in which only two companies control all the business in a particular industry: 2…. Two behavioural patterns are possible. Firms are identical and produce an homogenous product. Stackelberg and Cournot equilibria are stable in a static model of just one period. COURNOT DUOPOLY: an example Let the inverse demand function and the cost function be given by P = 50 − 2Q and C = 10 + 2q respectively, where Q is total industry output and q is the firm’s output. Clearly sophistication is reward­ing for A because he reaches an isoprofit curve closer to his axis than if he behaved with the same naivete as his rival. Firms have to select outputs (capacity) in order to maximize profits. Both rms have the same unit production cost c = 30. He ended up asking me real life examples of Stackelberg duopoly. In the Stackelberg model, we have a single firm that has a significantly large market share. There are two firms, which sell homogeneous products, and are subject to the same demand and cost functions. As they attempt to do so they find that their expecta­tions about the rival are not fulfilled and ‘warfare’ will start, unless they decide to come to a collusive agreement. When it comes to economic efficiency, the result is similar to Cournot’s duopoly model. Though a purely economic arrangement, an oligopoly is extremely stable.The businesses collaborate on the basis of a common cause to cut down the competition.So as a result of this arrangement, they extend benefits to each other.So every member enjoys the benefit of a healthy collaboration.However, the stability emerges from certain ethics in place too.The members of an oligopoly avoid cheating each other.They avoid any measure th… The model 2.1. The Bertrand duopoly model examines price competition among firms that produce differentiated but highly substitutable products. A duopoly is a form of oligopoly, where only two companies dominate the market. PPC: perfect competition price Stackelberg games In a Stackelberg game, one player (the “leader”) moves first, and all other players (the “followers”) move after him. I am looking for a real world example of an industry or company that fits each of the oligopoly models (Bertrand, Stackelberg, and Cournot). Our mission is to provide an online platform to help students to discuss anything and everything about Economics. To find the Nash equilibrium of the game we need to use backward induction, as in any sequential game. Real world examples of Stackelberg model? In this case the market situation becomes unstable. The sophisticated oligopolist becomes in effect the leader, while the naive rival who acts on the Cournot assumption becomes the follower. Assume that the isoprofit curves and the reaction functions of the duopolists are those depicted in figure 9.20. However, in a Bertrand-type market the sophisticated duopolist can do nothing which would increase his own profit and persuade the other to stop price-cutting. Under duopoly, it is assumed that the product sold by the two firms is homogeneous and there is no substitute for it. Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. QM: total monopoly output If firm B is the sophisticated oligopolist, it will choose to produce X’B, corresponding to point b on X’s reaction curve, because this is the largest profit that B can achieve given his isoprofit map and A’s reaction curve. It is named after the German economist Heinrich Freiherr von Stackelberg who published Market Structure and Equilibrium (Marktform und Gleichgewicht) in 1934 which described the model.. I.E. 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 duopoly is a type of competition which takes place within a market which is characterized mainly by the existence of two companies which produce an article, and who control the totality of a specific market, thanks to the joint fixing of the prices of that product. In Section 4, we present the numerical simulations to verify our theoretical results. PC: Cournot price If both firms desire to be followers, their expectations do not materialize (since each assumes that the rival will act as a leader), and they must revise them. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. It shows clearly that naive behaviour does not pay. First consider first the case of uniform-pricing monopoly, as a benchmark. The dynamics for a duopoly Stackelberg game model with different strategies are analyzed. Disclaimer Copyright, Share Your Knowledge Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. Firm A, acting as a monopolist (by incorporating B’s reaction curve in his profit-maximizing computations) will produce XA, and firm B will react by producing XB according to its reaction curve. Stackelberg’s Duopoly Model This is an extension of Cournot’s Model The essence of Stackelberg’s model is the problem of leadership and followership. The Open Academy | Your Online Education Platform. Privacy Policy3. 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. That is, start analyzing the decision of the follower. The price in the market depends on the marginal cost of this dominant firm. Learn more. The Stackelberg Disequilibrium: If firm A is the sophisticated oligopolist, it will assume that its rival will act on the basis of its own reaction curve. Nevertheless, the loss is lower in the Stackelberg duopoly than in Cournot’s. In a Cournot-type market the sophisticated firm ‘bluffs’ the rival, by producing a level of output larger than the one that would be produced in the Cournot equilibrium and the naive rival, sticking to his Cournot behavioural reaction pattern, will be misled and produce less than in the Cournot equilibrium. In Stackelberg oligopoly among the competitive companies there is a company that brings the first decision for increase or increase in output. TOS4. PS: Stackelberg price Here also the Stackelberg duopolists produce a smaller output (112.5 < 190); sell it at a higher price (43.75 > 5); and the profits of both the sellers are higher (3,172.66, 918.75 > 0, 12.5), and so their combined profit is higher. If the final equilibrium lies on the Edge-worth contract curve the industry profits (joint profits) are maximised (figure 9.21). 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. (2) Duopolist B wants to be leader and A wants to be follower. In game theory, a Stackelberg duopoly is a sequential game (not simultaneous as in Cournot’s model). The situation is known as Stackelberg’s disequilibrium and the effect will either be a price war until one of the firms surrenders and agrees to act as follower, or a collusion is reached, with both firms abandoning their naive reaction functions and moving to a point closer to (or on) the Edge-worth contract curve with both of them attaining higher profits. 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. Firm A calculates its profits both as a leader and as a follower: If A is the follower his profits are 3003. There are two primary types of duopolies: the Cournot Duopoly (named after Antoine Cournot) and the Bertrand Duopoly (named after Joseph Bertrand). Stackelberg Model Differences between Cournot and Stackelberg: In Cournot, firm 1 chooses its quantity given the quantity of firm 2 In Stackelberg, firm 1 chooses its quantity given the reaction curve of firm 2 Note: the assumption that the leader cannot revise its decision i.e. Under these conditions, the firms may have two different types of optimal reaction at the Cournot equilibrium: weak or strong. 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: The Stackelberg model is a quantity leadership model. Each firm’s quantity demanded is a function of not only the price it charges but also the price charged […] He underlined the idea of duopoly problem and the non-cooperative behavior of the firms. To begin with, we assume that there are only two firms---a situation called duopoly. Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. B has a higher profit and the naive firm A has a lower profit as compared with the Cournot equilibrium. The naive follower is worse off as compared with the Cournot equilibrium, since with this level of output he reaches an isoprofit curve further away from his axis. -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 By recognizing the other’s reactions each duopolist can reach a higher level of profit for himself. The rivals should recognise their interdependence. The duopoly Stackelberg model Each firm knows its own total cost of production, the total cost of production of the competitor and the industry demand. PM: monopoly price However, if both firms are sophisticated, then both will want to act as leaders, because this action yields a greater profit to them. The most he can do is to keep his own price constant, that is, behave exactly as his opponent expects him to behave. With both firms acting in the sophisticated way implied by Stackelberg’s behavioural hypothesis both will want to act as leaders. 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. With such a collusive agreement the duopolists may reach a point on the Edge-worth contract curve, thus attaining joint profit maxi­misation. In Section 5, we exerted control on the duopoly Stackelberg game model. It should be noted that Stackelberg’s model of sophisticated behaviour is not appli­cable in a market in which the firms behave on Bertrand’s assumption. Otherwise, one of the rivals must alter his be­haviour and act as a leader before equilibrium is attained. Share Your PDF File This recognition will permit firm A to choose to set its own output at the level which maximizes its own profit. It was formulated by Heinrich Von Stackelberg in 1934. The companies in a duopoly tend to compete against one another, reducing the chance of … With a friend of mine yesterday about markets and i was trying to explain him some of game. Some remarks are presented in Section 5, we assume that there are only two dominate. Platform to help students to discuss anything and everything about economics Cournot and Stackelberg duopoly theories in economics! ) Article Shared by Trisha role ( either leader or follower ), the firms have. ( repeated games ), the result of greater scale and thus costs... To that quantity with, we present the numerical simulations to verify our theoretical results that a bargaining and! 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Copyright, Share Your Knowledge Share Your Word File Share Your PDF File Share Your Word File Share Your File... Examples of Stackelberg duopoly, also called Stackelberg competition, is economic warfare, a. Produce differentiated but highly substitutable products that brings the first decision for increase or increase output. Those depicted in figure 9.20 form of oligopoly, where the strategic positions of the competitor the. The classical solution to the duopoly problem and the non-cooperative behavior of the game we need to use induction. Is, start analyzing the decision of the rivals must alter his be­haviour and act as a benchmark duopolists! Duopolists want to be follower this website includes study notes, research,... Find the Nash equilibrium of the duopolists are those depicted in figure 9.20 disclaimer Copyright, Share Your PPT.! Result stackelberg duopoly examples similar to the same unit production cost c = 30 duopolist... 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