However, this is example-specific. By differentiation, the maximum payoff is given by Whether by noncompetitive practices, government mandate or technological savvy, these companies take advantage of their position to increase their profitability. ( The fall of the US automobile companies is a burning example. {\displaystyle \Pi _{1}=P(q_{1}+q_{2}(q_{1})).q_{1}-C_{1}(q_{1})} 5000 = 2 ( ( is to be found. However, this very fact (that the follower would play non-Stackelberg if the leader were to play Stackelberg) means that this profile is not a Nash equilibrium of the subgame starting when the leader has already played Stackelberg (a subgame off the equilibrium path). 2 Oligopoly theory makes heavy use of game theory to model the behavior of oligopolies: Stackelberg's duopoly. This paper studies undesirable competition in an asymmetric Stackelberg oligopoly under both unit and ad valorem taxation. c) A single firm (the leader) selects an output before all other firms choose their outputs. In this model, the firms move sequentially (see Stackelberg competition). − Chamberlin’s Small Group Model 4. For a 2 Firm Stackelberg's oligopoly game, we can simply use the Best Response function of the follower firm and use it in the profit maximization function of leader's firm. 5000 q But the maximum amount of profits means choosing that point on firm 2’s reaction curve that touches firm l’s lowest attain­able iso-profit curve, as shown by point E in Fig. In fact, its best response (by the definition of Cournot equilibrium) is to play Cournot quantity. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] 24.5 we also show Cournot equilibrium point c, where the two reaction curves meet. {\displaystyle p_{1}} Indeed, it is the very thing that makes a Cournot strategy profile a Nash equilibrium in a Stackelberg game that prevents it from being subgame perfect. 2 − (1). Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. 1st Jan 1970 Economics Reference this Disclaimer: This work has been submitted by a university student. ∗ Oligopoly is defined as a market form in which a market is dominated by a small number of sellers. 1 An extensive-form representation is often used to analyze the Stackelberg leader-follower model. q 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. However, in equilibrium, it knows the follower will choose However, in an (indefinitely) repeated Stackelberg game, the follower might adopt a punishment strategy where it threatens to punish the leader in the next period unless it chooses a non-optimal strategy in the current period. q , i.e. More generally, the leader must have commitment power. 4 Out of these 4 types of oligopolies, which type would be better and most preferable to consumers? i 2 Content Filtration 6. Before uploading and sharing your knowledge on this site, please read the following pages: 1. The Bertrand duopoly model examines price competition among firms that produce differentiated but highly substitutable products. It assumes a generalised linear demand structure. Cournot Oligopoly - General Case. P The Stackelberg leader is sometimes referred to as the Market Leader. for the follower's best response function). A member of an oligopoly is called an oligopolist. − a. Cournot oligopoly. If the leader played a Stackelberg action, (it believes) that the follower will play Cournot. Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity s n ≥0 • Cost of producing s n: c n s n q Each firm’s quantity demanded is a function of not only the price it charges but also the price charged […] Abstract. 1 5000 Provide a real-world example of a market that approximates each of the following oligopoly settings, and explain your reasoning. 2 {\displaystyle \Pi _{1}} a. Cournot oligopoly. where the subscript 1 represents the leader and 2 represents the follower. − 1 5000 to maximise its payoff An alternative interpretation of Stackelberg independence is that firms in each period t behave as Cournotian oligopolists on the residual demand left by firms in earlier periods. Follower produces less than the Cournot equilibrium output. The demand function is linear and price elasticity of demand is 1. ) It is clear (if marginal costs are assumed to be zero - i.e. = You can view samples of our professional work here. Hence it is non-optimal for the leader to play Stackelberg. ∗ In recent years, Stackelberg games have contributed a lot in the security domain[1] where it is essential for the security personnel to protect some valuable resource and search for any potential threats to it. ) 3 So both desire to act as leaders. There are Two firms in the market, A and B 2. 1 Hence the market best suits to this type of oligopoly is the market for crude oil producing companies where there are few rival giants serving the entire market. Together, these companies control 89% of the US cellular phone market, as of 2014. In this model a follower obeys his reaction function q2 = f2 (q1) and adjusts his output level to maximise his profit, given the quantity decision of his rival, who he assumes to be a leader. The Cournot model is applicable to industries in which all firms are similar and none has a strong operating advantage or leadership position. 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. p given ( If the leader has already played Stackelberg, the best response of the follower is to play Stackelberg (and therefore it is the only action that yields a Nash equilibrium in this subgame). In Fig. 1 There are some further constraints upon the sustaining of a Stackelberg equilibrium. 24.4. 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. 2 In this then the Stackelberg model of oligopoly is seen. Both rms have the same unit production cost c = 30. There are many different models for oligopoly behaviour such as the Cournot Solution, the Sweezy Kinked Demand Curve Solution, the Stackelberg Model and the Bertrand Model. The advantage that firm 1 enjoyed by going first is often called the ‘first-mover advantage’. An oligopoly is much like a monopoly, in which only one company exerts control over most of a market. − c Thus, each firm might make the same assumption about its rival’s response. Suppose that firm 1 got to choose its output level with a complete information on how firm 2 would respond. 24.5 by using the iso-profit curves of firms only, which are a type of indifference curves. q with respect to Also referred to as a “decision tree”, the model shows the combination of outputs and payoffs both firms have in the Stackelberg game. Hence, the maximum of 1 − {\displaystyle q_{2}} A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. {\displaystyle \Pi _{2}} The leader would produce 2000 and the follower would produce 1000. Oligopoly. Only higher profits for firm 1 are associated with iso-profit curves which are lower down since firm 1’s profits will increase as firm 2’s output falls. c We use equation (7) to derive the iso-profit curves in Fig. However, playing Cournot would not have been the best response of the leader were it that the follower would play Stackelberg if it (the leader) played Stackelberg. q 6 a) The market is contestable. one for Bertrand, one for Stackelberg … This is because once leader has committed to an output and observed the followers it always wants to reduce its output ex-post. (by substituting For example, the automobile industry is an oligopoly because there are a limited number of producers, but more than two, who must respond to worldwide demand. q given the best response function of the follower (firm 2), the output that maximises the leader's profit is found. With imperfect information, the threats described above can be credible. Examples of Oligopoly Markets. The locus of all the tangency points such as E, F, G and H is the reaction curve of firm 2, i.e., f2(q1). 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. The Cournot solution is obtained by maximising π1 with respect to q1, assuming q2 to be constant, and with respect to q2, assuming q1 to be constant. Cournot Bertrand And Stackelberg Models Of Oligopoly Economics Essay. Each firm is aware of the fact that equilibrium price in the market depends on total output produced. 1 The Stackelberg model is about strategic competition. We compare an m-firm Cournot model with a hierarchical Stackelberg model where m Firms choose outputs sequentially. Taking the first order derivative and equating it to zero (for maximisation) yields q So the follower just takes it as a constant. Using asymmetric Stackelberg oligopoly models, Pal and Sarkar (2001) and Mukherjee and Zhao (2009) show the possibilities of increases in existing firms' profits by entry. q 2 Sweezy’s Kinked Demand Model. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. This threat may be credible because it could be rational for the follower to punish in the next period so that the leader chooses Cournot quantities thereafter. Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. q The leader must know ex ante that the follower observes its action. ( 1 q − There is an obvious gain from being a market leader and being able to ‘move first’. q 1- Microsoft. Even my books from Uni didn't have any example. His duopoly model consists of two firms marketing a homogenous good. A real life example of this would be with Apple. Stackelberg Summary Stackelberg model illustrates how commitment can enhance profits in strategic environments. So in fact the leader wants to maximise its payoff But in the Stackelberg model, the firms set their quantities sequentially instead of … / is to be found. Cournot’s Duopoly Model 2. This would give the leader a profit (payoff) of two million and the follower a profit of one million. ( − {\displaystyle C_{i}(q_{i})} This implies that for each level of q1, firm 2 will choose the value of q2 which enables it to move the iso-profit curve furthest to the left, as shown in Fig. 2 Once the leader has chosen, the follower is better off by playing on the equilibrium path. q 2 It was formulated by Heinrich Von Stackelberg in 1934. Plagiarism Prevention 5. Thus total profit is the same as total revenue because total cost is zero. Hence the strategy profile - which is Cournot - is not subgame perfect. The most interesting set of assumptions about conjectural variation has been made in the analysis of leadership and followership formulated by the German economist Heinrich von Stackelberg. In game theory terms, the players of this game are a leader and a follower and they compete on quantity. Oligopoly is defined as a market form in which a market is dominated by a small number of sellers. However, when I repeat the procedure with a 3 firm Stackelberg's game, the results seem inconclusive. Assume two firms, where Firm One is the leader and produces \(Q_1\) units of a homogeneous good. In an oligopoly, there are at least two firms controlling the market.The retail gas market is a good example of an oligopoly because a small number of firms control a large majority of the market. P The Bertrand duopoly model examines price competition among firms that produce differentiated but highly substitutable products. In case of linear demand the inverse demand function takes the form p(q1 + q2) = a – b(q1 + q2). In part (b) (small) the quantity the follower produces is its best response to the leader’s output, as given by its Cournot best-response (or reaction) curve. Being a follower, firm 2 will choose an output along its reaction curve, f2(q1). p In order for the leader to make a rational decision about its own production, it has to consider the follower’s profit-maximisation problem. b. Stackelberg oligopoly – In a Stackelberg oligopoly, there is one firm which assumes the leader role and the other firms follow in their footsteps. P The Stackelberg model highlighted the value of (extra) information and the potential value of being a market leader, in the sense of being able to act first in setting output. q Airlines are not a duopoly but they are definitely an example of an oligopoly where the market is approaching perfect competition. The best response is to find the value of {\displaystyle p_{2}} Credible and non-credible threats by the follower, Mathematical programming with equilibrium constraints, https://en.wikipedia.org/w/index.php?title=Stackelberg_competition&oldid=979640436, Creative Commons Attribution-ShareAlike License, The aggregate Stackelberg output is greater than the aggregate Cournot output, but less than the aggregate. : The following example is very general. c As mentioned, imperfect information in a leadership game reduces to Cournot competition. Simply by moving first, the leader has accrued twice the profit of the follower. Disclaimer 8. A leader does not obey his reaction function q1 = f1(q2). 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