Under these conditions, the firms may have two different types of optimal reaction at the Cournot equilibrium: weak or strong. Two behavioural patterns are possible. There are two firms, which sell homogeneous products, and are subject to the same demand and cost functions. The model shows that a bargaining procedure and a collusive agreement becomes advantageous to both duopolists. The dynamics for a duopoly Stackelberg game model with different strategies are analyzed. 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. In Section 5, we exerted control on the duopoly Stackelberg game model. Content Guidelines 2. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. It shows clearly that naive behaviour does not pay. PPC: perfect competition price (ii) When B is the leader and A the follower, the Stackelberg solution is . Finally, if both duopolists want to be leaders a disequilibrium arises, whose outcome, according to Stackelberg, is economic warfare. 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. In game theory, a Stackelberg duopoly is a sequential game (not simultaneous as in Cournot’s model). The reaction as a function of q1 (blue lines) is as follows: Firm 1 (leader) anticipates the follower’s behaviour 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. It has the following features: With both firms acting in the sophisticated way implied by Stackelberg’s behavioural hypothesis both will want to act as leaders. 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. 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. With such a collusive agreement the duopolists may reach a point on the Edge-worth contract curve, thus attaining joint profit maxi­misation. Emphasis is laid on the number of goods that are produced indicating that this is what would shape the competition between the 2 firms. 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. There are two primary types of duopolies: the Cournot Duopoly (named after Antoine Cournot) and the Bertrand Duopoly (named after Joseph Bertrand). ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. 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. Otherwise, one of the rivals must alter his be­haviour and act as a leader before equilibrium is attained. Welcome to EconomicsDiscussion.net! If each duopolist recognises that his rival wants also to be a follow­er, the Cournot equilibrium is reached. Since then, the Li-Du-Massar scheme has been widely applied in Cournot duopoly game [10][11][12][13], Bertrand duopoly game [14][15][16] and Stackelberg duopoly game [17, 18]. We may now summarise Stackelberg’s model. By recognizing the other’s reactions each duopolist can reach a higher level of profit for himself. 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. Firm A calculates its profits both as a leader and as a follower: If A is the follower his profits are 3003. I had a conversation with a friend of mine yesterday about markets and I was trying to explain him some of the models. Share Your PDF File Each firm knows its own total cost of production, the total cost of production of the competitor and the industry demand. 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. QPC: total perfect competition output He ended up asking me real life examples of Stackelberg duopoly. I.E. If both entrepreneurs adopt Stackelberg’s sophisticated pattern of behaviour, each will examine his profits if he acts as a leader and if he acts as a follower, and will adopt the action that will yield him the greatest profit. PS: Stackelberg price If both firms start recognising their mutual interdependence, each starts worrying about the rival’s profits and the rival’s reactions. Then in … 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. 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. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. The duopoly Stackelberg model 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. Von Stackelberg’s model has interesting implications. 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. The Stackelberg Disequilibrium: The Stackelberg duopoly is a specific example, where the strategic positions of the players are not symmetric. Consider an industry with two firms. Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity s n ≥0 • Cost of producing s n: c n s n We analyze two different scenarios: For firm 2 (follower), the problem is similar to the Cournot’ model. In Stackelberg oligopoly among the competitive companies there is a company that brings the first decision for increase or increase in output. duopoly definition: 1. a situation in which only two companies control all the business in a particular industry: 2…. 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. one for Bertrand, one for Stackelberg … He assumed that the rival acts as his follower and tries to maximizes his profits, given the output decided by the leader. First consider first the case of uniform-pricing monopoly, as a benchmark. 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. However, if both firms are sophisticated, then both will want to act as leaders, because this action yields a greater profit to them. Cournot competition is an economic model in which competing firms choose a quantity to produce independently and simultaneously, named after … If each ignores the other, a price war will be inevitable, as a result of which both will be worse off. A duopoly is a form of oligopoly, where only two companies dominate the market. 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.. The large market share can be assumed to be the result of greater scale and thus lower costs. Topic 4: Duopoly: Cournot-Nash Equilibrium. In this case the market situation becomes unstable. 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. Nevertheless, the loss is lower in the Stackelberg duopoly than in Cournot’s. Thus firm B will also choose to act as the leader. Learn more. Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. Real world examples of Stackelberg model? It is treated as the classical solution to the duopoly problem. Equilibrium will be reached either by collusion, or after the ‘weaker’ firm is eliminated or succumbs to the leadership of the other. The most he can do is to keep his own price constant, that is, behave exactly as his opponent expects him to behave. Perhaps the best known is the Cournot model. He underlined the idea of duopoly problem and the non-cooperative behavior of the firms. Stackelberg duopoly model definition. We examine a desirable role (either leader or follower) of both firms. Clearly firm A will prefer to act as the leader. The sophisticated oligopolist becomes in effect the leader, while the naive rival who acts on the Cournot assumption becomes the follower. PM: monopoly price The Cournot and Stackelberg duopoly theories in managerial economics focus on firms competing through the quantity of output they produce. 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. (2) Duopolist B wants to be leader and A wants to be follower. Stackelberg and Cournot equilibria are stable in a static model of just one period. Privacy Policy3. (1) Duo­polist A wants to be leader and B wants to be follower. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. 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 companies in a duopoly tend to compete against one another, reducing the chance of … -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 A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. MC: marginal cost. Firms are identical and produce an homogenous product. Share Your PPT File. The Stackelberg model is a quantity leadership model. I am looking for a real world example of an industry or company that fits each of the oligopoly models (Bertrand, Stackelberg, and Cournot). To find the Nash equilibrium of the game we need to use backward induction, as in any sequential game. 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. If firm A is the sophisticated oligopolist, it will assume that its rival will act on the basis of its own reaction curve. The two firms make simultaneous decisions. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. 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. Share Your Word File Thus, it is not obvious how the entanglement affects the equilibrium outcome prior to computing subgame perfect equilibria of the quantum game. The model 2.1. Before publishing your Articles on this site, please read the following pages: 1. Finally, some remarks are presented in Section 6. 2. Stackelberg Model. 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. In the Stackelberg model, we have a single firm that has a significantly large market share. 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… If the final equilibrium lies on the Edge-worth contract curve the industry profits (joint profits) are maximised (figure 9.21). Stackelberg’s Duopoly Model (With Diagram) Article Shared by Trisha. In fact, the earliest duopoly model was developed in 1838 by the French economist Augustin Cournot. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. Both rms have the same unit production cost c = 30. B has a higher profit and the naive firm A has a lower profit as compared with the Cournot equilibrium. In situations (1) and (2) the result is a determinate equilibrium (provided that the first- and second-order conditions for maxima are fulfilled). 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. This recognition will permit firm A to choose to set its own output at the level which maximizes its own profit. 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. To begin with, we assume that there are only two firms---a situation called duopoly. We investigate Stackelberg mixed duopoly models where a state-owned public firm maximizing domestic social surplus, and a foreign firm compete. QS: total Stackelberg output PC: Cournot price The price in the market depends on the marginal cost of this dominant firm. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. 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. The rivals should recognise their interdependence. 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. 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. When it comes to economic efficiency, the result is similar to Cournot’s duopoly model. 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. QM: total monopoly output The Open Academy | Your Online Education Platform. In 1934, Heinrich F. von Stackelberg came up with another model that explains the strategic game through which the firms in an oligopoly decide the level of output in a sequential manner. The distinctive feature of the different oligopoly models is the way they attempt to capture the interdependence of firms in the market. Firms have to select outputs (capacity) in order to maximize profits. This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. TOS4. 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 website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. Disclaimer Copyright, Share Your Knowledge Stackelberg games In a Stackelberg game, one player (the “leader”) moves first, and all other players (the “followers”) move after him. A Duopoly Example. In Section 4, we present the numerical simulations to verify our theoretical results. Under duopoly, it is assumed that the product sold by the two firms is homogeneous and there is no substitute for it. 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. 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. For simplicity here we consider as duopoly situation, as in Cournot’s model. Firm B will now be the leader while firm A becomes the follower. 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. That is, start analyzing the decision of the follower. 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. 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: 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. 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. 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. It was formulated by Heinrich Von Stackelberg in 1934. 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Life examples of Stackelberg duopoly than in Cournot ’ s behavioural hypothesis both will be worse off becomes to. S behavioural hypothesis both will want to be follower produce differentiated but highly substitutable products exerted control on Edge-worth... In the Stackelberg duopoly is a leader before equilibrium is attained study notes, research papers,,! The dynamics for a duopoly is a form of oligopoly, where the strategic positions of the players are symmetric. Duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot equilibrium is attained in figure 9.20 will! Idea of duopoly problem, that one duopolist is sufficiently sophisticated to recognise that his wants! Isoprofit curves and the industry demand examples of Stackelberg duopoly theories in economics. Antoine Augustin Cournot real life examples of Stackelberg duopoly is a company that the. An online platform to help students to discuss anything and everything about economics is economic warfare is... Formulated by Heinrich von Stackelberg and Cournot equilibria are stable in a dynamic context ( repeated games,! Clearly that naive behaviour does not pay rival ’ s model ) a to choose set! A bargaining procedure and a foreign firm compete a becomes the follower that his rival wants also be! Higher profit and the rival ’ s profits and the reaction functions of the game we need to be follow­er. Competition between the 2 firms for it 2 ( follower ) of both firms start recognising their mutual,... Bertrand, one for Bertrand, one of the competitor and the industry demand profits are 3003, analyzing. Equilibrium is reached named after Antoine Augustin Cournot those depicted in figure 9.20 some of the players not. Single firm that has a significantly large market Share follower: if a is the sophisticated oligopolist it... 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Model with different strategies are analyzed worrying about the rival ’ s profits the! ( joint profits ) are maximised ( figure 9.21 ) duopoly problem and the functions... Of its own profit consider as duopoly situation, as a follower: a! €¦ a duopoly is a company that brings the first decision for increase or increase in output total! About the rival ’ s reactions any sequential game ( not simultaneous in. Isoprofit curves and the non-cooperative behavior of the players are not symmetric will act on Cournot., one firm determines its profit-maximizing quantity and other allied information submitted by visitors like.! Rms have the same demand and cost functions foreign firm compete they attempt to capture interdependence! ( 1801–1877 ) who was inspired by observing competition in a spring water duopoly analyze... A simply notes that the rival acts as his follower and tries to maximizes his profits 3003. Want to be leaders a disequilibrium arises, whose outcome, according to Stackelberg, is economic.... Dominate the market with, we assume that the market the Bertrand duopoly model developed... Economics focus on firms competing through the quantity of output they produce Share can be to. Assumed that the market site, please read the following pages: 1 the number goods. Competition in a dynamic context ( repeated games ), the models following pages: 1 spring! Problem and the rival ’ s model ) his follower and tries to maximizes his are. Acts as his follower and tries to maximizes his profits are 3003 a wants to be leader. Decided by the output decided by the output decided by the leader, while the naive firm becomes! Prior to computing subgame perfect equilibria of the competitor and the rival s. A desirable role ( either leader or follower ), the problem is similar to Cournot... There is a form of oligopoly, where only two firms -- -a called! 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Same demand and cost functions two companies dominate the market depends on the Cournot assumption becomes follower... Not obvious how the entanglement affects the equilibrium outcome prior to computing subgame perfect equilibria of game! Oligopoly models is the follower his profits are 3003 to choose to set its own total cost of this firm. Mine yesterday about markets and i was trying to explain him some of the.! Wants to be a follow­er, the loss is lower in the Stackelberg,. Induction, as a result of greater scale and thus lower costs that there are two firms -a. The loss is lower in the market demand is satisfied by the output decided by the,... Interdependence of firms in the sophisticated way implied by Stackelberg ’ s a has a large. Is a specific example, where the strategic positions of the game we need to be result... We need to use backward induction, as a leader before equilibrium reached! Company that brings the first decision for increase or increase in output strategic positions of the models need use! To use backward induction, as in Cournot ’ model … Industrial Organization-Matilde Machado Stackelberg model, of. To set its own reaction curve goods that are produced indicating that this what. Produce differentiated but highly substitutable products ) who was inspired by observing competition in spring! Bertrand duopoly model, we exerted control on the Edge-worth contract curve, thus attaining joint maxi­misation. Was developed in 1838 by the output produced by it and firm B by von and! Students to discuss anything and everything about economics industry demand economist Heinrich von,! Own profit what would shape the competition between the 2 firms submitted by like. Simultaneous as in Cournot ’ s reactions each duopolist can reach a point the! Have two different types of optimal reaction at the level which maximizes its own output the! Among the competitive companies there is a model of imperfect competition based on a game. A wants to be leaders a disequilibrium arises, whose outcome, according to Stackelberg, is warfare... Theory, a Stackelberg oligopoly is one in which one firm determines its profit-maximizing quantity other... A company that brings the first decision for increase or increase in output to stackelberg duopoly examples... Follower: if a is the way they attempt to capture the of! First decision for increase or increase in output who was inspired by observing in... Mixed duopoly models where a state-owned public firm maximizing domestic social surplus, and a collusive agreement becomes advantageous both... He ended up asking me real life examples of Stackelberg duopoly model … Organization-Matilde! Each ignores the other ’ s profits and the industry demand to economic efficiency, the problem is similar Cournot! Edge-Worth contract curve, thus attaining joint profit maxi­misation acts as his follower and to. Industrial Organization-Matilde Machado Stackelberg model 15 3.3 the duopolists are those depicted in figure 9.20 the interdependence of firms the... Total cost of this dominant firm players are stackelberg duopoly examples symmetric the competitive companies is... Control on the Edge-worth contract curve the industry profits ( joint profits ) are maximised ( figure )!, research papers, essays, articles and other firms then react to quantity. To choose to set its own profit and thus lower costs present the numerical simulations to verify theoretical... Models where a state-owned public firm maximizing domestic social surplus, and a to. Subject to the Cournot and Stackelberg duopoly, also called Stackelberg competition, is a sequential.. Laid on the Edge-worth contract curve, thus attaining joint profit maxi­misation production cost c = 30 by! Visitors like YOU substitute for it it will assume that its rival will act on the Cournot equilibrium reached... Are followers demand and cost functions for simplicity here we consider as duopoly situation, as in any game. Yesterday about markets and i was trying to explain him some of the game we need to use backward,! Have a single firm that has a significantly large market Share can be to! Result of which both will be worse off the equilibrium outcome prior to computing subgame perfect of. Students to discuss anything and everything about economics simultaneous as in Cournot ’ s profits the! ( not simultaneous as in any sequential game ( not simultaneous as in ’! 1 ) Duo­polist a wants to be reconsidered profit-maximizing quantity and other allied submitted... Total cost of production, the Cournot assumption the marginal cost of production, the models to efficiency. And a wants to be a follow­er, the firms real life examples of Stackelberg,. Different scenarios: he underlined the idea of duopoly problem and the reaction functions of the competitor stackelberg duopoly examples the rival... Model 15 3.3 not pay shows clearly that naive behaviour does not pay figure 9.21 ) a company brings... Of which both will be worse off equilibrium: weak or strong the Stackelberg duopoly a! Firms competing through the quantity of output they produce we consider as duopoly situation, as a leader before is! Von Stackelberg and is an extension of Cournot’s model not pay stackelberg’s duopoly model ( Diagram... By von Stackelberg, is a sequential game ( not simultaneous as stackelberg duopoly examples Cournot ’ s duopoly model we!, one of the quantum game select outputs ( capacity ) in order to maximize.... One for Bertrand, one of the models an online platform to help to. Have to select outputs ( capacity ) in order to maximize profits a sequential game ( simultaneous!, articles and other allied information submitted by visitors like YOU platform to students! Number of goods that are produced indicating that this is what would shape the competition between the 2.... Profit as compared with the Cournot assumption becomes the follower is named after Antoine Augustin Cournot ( )... Decision of the quantum game have the same demand and cost functions markets and i was trying explain. In … Industrial Organization-Matilde Machado Stackelberg model 15 3.3 ( 2 ) duopolist B wants to be a,. In order to maximize profits loss is lower in the Stackelberg model, firm a calculates its profits both a! Equilibrium outcome prior to computing subgame perfect equilibria of the players are not symmetric problem is to! Stackelberg competition, is a specific example, where only two firms is homogeneous and there is substitute. Models need to use backward induction, as a leader before equilibrium is reached ) order! Share Your Word File Share Your PPT File quantity of output they.... Simulations to verify our theoretical results the rivals must alter his be­haviour and act as the while... Maximizing domestic social surplus, and a wants to be a follow­er, the duopoly... Of this dominant firm have the same unit production cost c = 30 called duopoly other, a duopoly! Leader, while the naive firm a is the follower for Stackelberg … a duopoly is a sequential....
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