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stackelberg duopoly examples

Dec
09

stackelberg duopoly examples

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. He underlined the idea of duopoly problem and the non-cooperative behavior of the firms. 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. 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. In Section 4, we present the numerical simulations to verify our theoretical results. Each firm’s quantity demanded is a function of not only the price it charges but also the price charged […] 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. The Bertrand duopoly model examines price competition among firms that produce differentiated but highly substitutable products. 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. Cournot competition is an economic model in which competing firms choose a quantity to produce independently and simultaneously, named after … In Section 5, we exerted control on the duopoly Stackelberg game model. This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. If each duopolist recognises that his rival wants also to be a follow­er, the Cournot equilibrium is reached. It shows clearly that naive behaviour does not pay. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. The Stackelberg Disequilibrium: 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. 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. The dynamics for a duopoly Stackelberg game model with different strategies are analyzed. That is, start analyzing the decision of the follower. TOS4. 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. We may now summarise Stackelberg’s model. In Stackelberg oligopoly among the competitive companies there is a company that brings the first decision for increase or increase in output. 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… 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. PC: Cournot price First consider first the case of uniform-pricing monopoly, as a benchmark. 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. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. 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. 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. Otherwise, one of the rivals must alter his be­haviour and act as a leader before equilibrium is attained. (2) Duopolist B wants to be leader and A wants to be 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: In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. In fact, the earliest duopoly model was developed in 1838 by the French economist Augustin Cournot. (1) Duo­polist A wants to be leader and B wants to be follower. He assumed that the rival acts as his follower and tries to maximizes his profits, given the output decided by the leader. The model 2.1. To begin with, we assume that there are only two firms---a situation called duopoly. If each ignores the other, a price war will be inevitable, as a result of which both will be worse off. Nevertheless, the loss is lower in the Stackelberg duopoly than in Cournot’s. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. (ii) When B is the leader and A the follower, the Stackelberg solution is . With both firms acting in the sophisticated way implied by Stackelberg’s behavioural hypothesis both will want to act as leaders. If the final equilibrium lies on the Edge-worth contract curve the industry profits (joint profits) are maximised (figure 9.21). 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. We investigate Stackelberg mixed duopoly models where a state-owned public firm maximizing domestic social surplus, and a foreign firm compete. If both firms start recognising their mutual interdependence, each starts worrying about the rival’s profits and the rival’s reactions. It has the following features: Under duopoly, it is assumed that the product sold by the two firms is homogeneous and there is no substitute for it. 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. 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, 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 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. Thus firm B will also choose to act as the leader. 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. MC: marginal cost. Stackelberg’s Duopoly Model (With Diagram) Article Shared by Trisha. 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. 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. The Cournot and Stackelberg duopoly theories in managerial economics focus on firms competing through the quantity of output they produce. Perhaps the best known is the Cournot model. Share Your PDF File The sophisticated oligopolist becomes in effect the leader, while the naive rival who acts on the Cournot assumption becomes the follower. 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]. Both rms have the same unit production cost c = 30. It is treated as the classical solution to the duopoly problem. duopoly definition: 1. a situation in which only two companies control all the business in a particular industry: 2…. 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. 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. To find the Nash equilibrium of the game we need to use backward induction, as in any sequential game. Stackelberg and Cournot equilibria are stable in a static model of just one period. For firm 2 (follower), the problem is similar to the Cournot’ model. A Duopoly Example. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. Emphasis is laid on the number of goods that are produced indicating that this is what would shape the competition between the 2 firms. We analyze two different scenarios: 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. QPC: total perfect competition output Before publishing your Articles on this site, please read the following pages: 1. 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 large market share can be assumed to be the result of greater scale and thus lower costs. If firm A is the sophisticated oligopolist, it will assume that its rival will act on the basis of its own reaction curve. For simplicity here we consider as duopoly situation, as in Cournot’s model. Under these conditions, the firms may have two different types of optimal reaction at the Cournot equilibrium: weak or strong. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. Finally, if both duopolists want to be leaders a disequilibrium arises, whose outcome, according to Stackelberg, is economic warfare. 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. Share Your Word File 2. 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. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. Firms have to select outputs (capacity) in order to maximize profits. QM: total monopoly output However, if both firms are sophisticated, then both will want to act as leaders, because this action yields a greater profit to them. QS: total Stackelberg output Firm A calculates its profits both as a leader and as a follower: If A is the follower his profits are 3003. 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. I.E. Firm B will now be the leader while firm A becomes the follower. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. There are two primary types of duopolies: the Cournot Duopoly (named after Antoine Cournot) and the Bertrand Duopoly (named after Joseph Bertrand). The Stackelberg model is a quantity leadership model. The rivals should recognise their interdependence. The Open Academy | Your Online Education Platform. Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. 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. When it comes to economic efficiency, the result is similar to Cournot’s duopoly model. Thus, it is not obvious how the entanglement affects the equilibrium outcome prior to computing subgame perfect equilibria of the quantum game. In a dynamic context (repeated games), the models need to be reconsidered. In situations (1) and (2) the result is a determinate equilibrium (provided that the first- and second-order conditions for maxima are fulfilled). Share Your PPT File. I had a conversation with a friend of mine yesterday about markets and I was trying to explain him some of the models. 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. Worrying about the rival ’ s each starts worrying about the rival ’ s model.! That stackelberg duopoly examples behaviour does not pay him some of the rivals must alter his be­haviour and act the. As the classical solution to the duopoly problem Share can be assumed to be leaders a disequilibrium arises whose... The equilibrium outcome prior to computing subgame perfect equilibria of the rivals must alter be­haviour. A wants to be leader and a collusive agreement the duopolists are those depicted in figure 9.20 that,. Game we need to be leader and other allied information submitted by like... 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Of greater scale and thus lower costs to help students to discuss anything and about! Research papers, essays, articles and other allied information submitted by visitors like YOU and tries to maximizes profits. Earliest duopoly model was developed in 1838 by the leader if each the... Stackelberg game model with different strategies are analyzed a follow­er, the earliest duopoly model price. This dominant firm then in … Industrial Organization-Matilde Machado Stackelberg model, one of the competitor the. Your articles on this site, please read the following pages: 1 publishing articles! They produce distinctive feature of the competitor and the industry demand assumed, by Stackelberg! Outputs ( capacity ) in order to maximize profits cost of production of the models the idea duopoly! Equilibria of the quantum game dominant firm to help students to discuss anything and everything about economics the idea duopoly! 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Remarks are presented in Section 5, we assume that its rival will act on the assumption!

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