Formally we can express this with the following demand function for Fast Gas: [latex]Q_F \left\{\begin{matrix} & & & \\ a-bP_F\,\,if\,\,P_F< P_S & & & \\ \frac{a-bP}{2}\,\,ifP_F=P_S & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.[/latex]. So we have to start at the second move of the game: National’s output choice. Can policy correct the situation and lead to a mutually beneficial outcome? Figure 17.3.3: The Sequential Market Entry Game. 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. They could instead set PF=PS and get ½ the demand at that price and make a positive profit. In the mid two thousands banks in the United States found themselves struggling to satisfy a tremendous demand for mortgages from the market for mortgage back securities: securities that were created from bundles of residential or commercial mortgages. We’ll call them Federal Gas and National Gas. 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 Nota: the assumption that the leader cannot revise its decision i.e. Get step-by-step explanations, verified by experts. Depicting the Stackelberg outcome (both firms produce) x 2 quantities in a Stackelberg equilibrium C S x 1 26 Exercise (Equilibria) Which is an equilibrium in the Stackelberg model? This is known as a 'Stackelberg leadership’ model. 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. Let’s return to the example of two oil companies: Federal Gas and National Gas. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex], [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex], [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N[/latex]. But the discipline of the market assumes that rewards are absolute that returns are not based on relative performance that the environment is not strategic. And since both the quantity produced and the price received are lower for the Stackelberg follower compared to the Cournot outcome, the profits must be lower as well. Interestingly, this banking crisis came relatively soon after a series of reforms of banking regulations in the United States that gave banks much more freedom in their operations. Remember that best response functions are one player’s optimal strategy choice given the strategy choice of the other player. Oligopolists face downward sloping demand curves which means that price is a function of the total quantity produced which, in turn, implies that one firm’s output affects not only the price it receives for its output but the price its competitors receive as well. If you include the cost to society of bailing out high-risk banks when they fail, the second-best outcome is that much worse. We can solve these by substituting one equation into the other which yields a single equation with a single unknown: [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}[\frac{A-c}{2B}-\frac{1}{2}q_F][/latex], [latex]q^*_F=\frac{A-c}{2B}-\frac{A-c}{4B}+\frac{1}{4}q_F[/latex], [latex]\frac{3}{4}q^*_F=\frac{A-c}{4B}[/latex], The Nash equilibrium is: [latex](q^*_F,q^*_N)[/latex] , or [latex](\frac{A-c}{3B} , \frac{A-c}{3B})[/latex]. 18.2 Bertrand Model of Oligopoly: Price Setters. The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. Do you think that government regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets gone bad. To do so we have to begin with a best response function. The Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. By Robert J. Graham The Stackelberg model of oligopoly within managerial economics illustrates one firm’s leadership in an oligopoly. Module 1: Preferences and Indifference Curves, Module 5: Individual Demand and Market Demand, Module 6: Firms and their Production Decisions, Module 10: Market Equilibrium – Supply and Demand, Module 11: Comparative Statics - Analyzing and Assessing Changes in Markets, Module 18: Models of Oligopoly – Cournot, Bertrand and Stackleberg. [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}q_F[/latex], When it comes to Federal’s decision, we diverge from the Cournot model because instead of taking qN as a given, Federal knows exactly how National will respond because they know the best response function. As long as the prices are above c there is always an incentive for both stations to undercut each other’s price, so there is no equilibrium. It's like Cournot, but there is a leader' firm choosing a quantity first; this is observed by a 'follower' firm, which then sets its quantity. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. Let’s assume that Fast Gas and Speedy Gas both have the same constant marginal cost of c, and will assume no fixed costs to keep the analysis simple. Since the Cournot outcome is one of the options for the Stackleberg leader – if it chooses the same output as in the Cournot case the follower will as well – it must be true that profits are higher for the Stackelberg leader. By symmetry, National Oil has an identical best response function: [latex]\color{green} q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex], We know from Module 15 that the monopolists marginal revenue curve when facing an inverse demand curve P=A-BQ. 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. From the consumer’s perspective, the Stackelberg outcome is preferable because overall there is more quantity at a lower price. 8. This is because in the Cournot case both firms took the other’s output as given. We will assume that each liter of gas produced costs the company c, or that c is the marginal cost of producing a liter of gas for both companies and that there are no fixed costs. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. When National makes this decision, Federal’s output choices is already made and known to National so it is takes as given. This module considers all three in order beginning with the Cournot model. The rationale was increased competition and the discipline of the market would inhibit excessive risk-taking and so stringent government regulation was no longer necessary. Why do you think that banks were so willing to engage in risky bets in the early 2000nds? Lets imagine a simple situation where there two gas stations, Fast Gas and Speedy Gas on either side of a busy main street. Are there any additional Nash equilibria ? But in the Stackelberg model, the firms set their quantities sequentially instead of simultaneously. Stackelberg Model. C. one firm plays a leadership role and its rivals merely react to the leader's quantity. The marginal revenue function that is associated with this is: We know marginal cost is 400, so setting marginal revenue equal to marginal cost results in the following expression: This is the best response function for Federal Oil. Table 13.1: Metrics of the Four Basic Market Structures Course Hero is not sponsored or endorsed by any college or university. For simplicity here we consider as duopoly situation, as in Cournot’s model. By being able to set its quantity first, Federal Oil is able to gain a larger share of the market for itself and even though it leads to a lower price, it makes up for that lower price with the increase in quantity to achieve higher profits. This is because the rewards are relative. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] Problem Set 4-EC 401-Fall 2020-Answers.pdf, EC401-Lecture 11-Applications of SPNE-Chapter 15 and 16-2020-revised.pdf, EC401-Lecture 9-Applications of Nash Equilibrium-Chapter 10-2020.pdf. Stackelberg duopoly model definition The gas they produce is identical but now they decide their output levels sequentially. 18.1 Cournot Model of Oligopoly: Quantity Setters. The Stackelberg model has an irreversible nature, that is to say it involves permanent action or commitment of agents where later movers observe the moves or action of the first movers, and then acti in the game. The weekly demand for wholesale gas is still P = A – BQ , where Q is the total quantity of gas supplied by the two firms or, Q=qF+qN. Being a high-risk bank when your competitor is a low-risk bank brings a big reward; the relatively high returns are compounded by the reward from the stock market. This will depend on both the firm’s own output and the competing firm’s output. The example here are the retail gas stations that bought the wholesale gas from the refiners and are now ready to sell it to consumers. Assume that Raphael and Susan can collect and sell a large quantity of eggs at no cost and that free-range eggs sold outside Pasturetown cannot be transported into the town for sale. We will again call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. [latex]\color{green} \frac{\partial \pi_F}{\partial q_F}=0[/latex], If πF = qF ( A – B ( qF + qN ) -c ) then we can expand to find, Taking the partial derivative of this expression with respect to qF, [latex]\color{green}\frac{\partial \pi_F}{\partial q_F}=A-2Bq_F-Bq_N-c=0[/latex]. The model we use to analyze this is one first introduced by French economist and mathematician Antoine Augustin Cournot in 1838. The opposite is true for the second mover, by being forced to choose after the leader has set its output, the follower is forced to accept a lower price and lower output. Total output is the sum of the two and is 200 thousands gallons. Both the Cournot model and the Bertrand model assume simultaneous move games. So where is the correspondence of best response functions? Policy Example: How Should the Government Have Responded to Big Oil Company Mergers? What is the Stackelberg Model? Interestingly, the solution to the Cournot model is the same as the more general Nash equilibrium concept introduced by John Nash in 1949 and the one used to solve for equilibrium in non-cooperative games in Module 17. When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. , then we can find the optimal output level by solving for the stationary point, or solving: [latex]\color{green} \pi_F=Aq_F-Bq\frac{F}{2}-Bq_Fq_N-cq_F[/latex], Taking the partial derivative of this expression with respect to. So [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. The Cournot model considers firms that make an identical product and make output decisions simultaneously. There are three main models of oligopoly markets, each consider a slightly different competitive environment. This module considers all three in order beginning with the Cournot model. 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. This preview shows page 1 - 2 out of 2 pages. This makes sense when one firm has to make a strategic decision before knowing about the strategy choice of the other firm. The gas they produce is identical and they each decide independently, and without knowing the other’s choice, the quantity of gas to produce for the week at the beginning of each week. The question we now have to answer is what are the best response functions for the two stations? Simplifying yields: [latex]\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)[/latex]. Clearly, this third option is the one that yields the most profit. Intermediate Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. The Bertrand Model: what happens when two firms compete simultaneously on … Stackelberg Model Practice Question: Consider the stackelberg model in which °rm 1 sets a quantity q 1 °rst, followed by °rm 2 which sets its own quantity q 2 after observing q 1: The market price is given by P = 40 ° Q; where Q = q 1 + q 2: Let each °rm±s MC =10. The Stackelberg model is a quantity leadership model. The number of firms is restricted to two by assuming barriers to entry. This, along with the low-interest rate policy of the Federal Reserve, led to a tremendous housing boom in the United States that evolved into a speculative investment bubble. An extensive-form game describing this problem is as follows: • 1 = {L,F}. Stackelberg model with entry deterrence In Pasturetown, only Raphael and Susan can raise free-range chickens on their farms. This is Federal Oil’s best response function, their profit maximizing output level given the output choice of their rivals. These twin crises led to the worst recession since the great depression. Hence the model was an alternative to Cournot Competition, with the Stackelberg Leadership Model resulting in lower Prices and greater total output Quantity. STACKELBERG INDEPENDENCE* Toomas Hinnosaar † The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. [latex]\color{green}A-2Bq_F-Bq_N=c[/latex]. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. The banks are better off and because the adverse effects of high-risk strategies going bad are taken away, society benefits as well. In this case the best response is the firm’s profit maximizing output. We will assume that Federal Gas sets its output first and then, after observing Federal’s choice, National Gas decides on the quantity of gas they are going to produce for the week. The Stackelberg leadership model is a model of a duopoly. 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. This is a system of two equations and two unknowns and therefore has a unique solution as long as the slopes are not equal. 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. Learning Objective 18.2: Describe normal form games and identify optimal strategies and equilibrium outcomes in such games. With these assumptions in place, we can express Federal’s profit function: Substituting the inverse demand curve we arrive at the expression. This means the price is lower because the demand curve is downward sloping. 4. Oligopoly markets are markets in which only a few firms compete, where firms produce homogeneous or differentiated products and where barriers to entry exist that may be natural or constructed. These graphical illustrations of the best response functions are called reaction curves. Therefore, we can express Federal’s profit function as: This is the same as in the Cournot example and for National the best response function is also the same. equilibrium outcome because it is a dynamic game)? Let’s consider a specific example. Answer: Each °rm±s pro°t function can be written as, We apply backward induction, that is, we solve °rm 2±s problem °rst given, The °rst order condition for °rm 2 can be written as, The equation above implicitly de°nes °rm 2±s best response function, Since we have derived how °rm 2 will respond to °rm 1±s output (which, is captured by °rm 2±s best response function. Stackelberg Model Note: When firms are symmetric, i.e. There is a considerable first-mover advantage. The weekly demand for wholesale gas in the Rocky Mountain region is P=A – BQ, where Q is the total quantity of gas supplied by the two firms or, Q=qF+qN. Therefore the leader firm has the advantage of higher profits, due to its high quantity. In this case A = 1,000, B = 2 and c = 400. is MR(q)=A-2Bq. Both stations have large signs that display the gas prices that each station is offering for the day. quantity of output they produce of a homogeneous good. In this paper, we discuss a retailer-supplier uncooperative replenishment model with a trade credit period when the demand and default risk are linked to the trade credit period in a supplier-Stackelberg game. So an individual gas station’s demand is conditional on its relative price with the other station. The answer in this case is a resounding ‘yes.’ If policy makers take away the ability of the banks to engage in high-risk strategies, the bad equilibrium will disappear and only the low-risk, low-risk outcome will remain. In the end, both banks end up choosing high-risk and are in a worse outcome than if they had chosen a low risk strategy because of the increased likelihood of negative events from the strategy. Most notably was the 1999 repeal of provisions of the Glass-Steagall Act, enacted after the beginning of the great depression in 1933, that prohibited commercial banks from engaging in investment activities. 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 Nota: the assumption that the leader cannot revise its decision i.e. Now that we know the best response functions solving for equilibrium in the model is relatively straightforward. [latex]q^*_N=150-\frac{(100)}{2}=100[/latex], [latex]\Pi _N=q_N(A-B(q_N+q_F)-c)[/latex], [latex]\color{green}\pi_F=q_F(A-B(q_F+q_N)-c)[/latex]. Stackelberg Model: The Stackelberg model is the quantity leadership model. The example we used in that section was wholesale gasoline where the market sets a price that equates supply and demand and the strategic decision of the refiners was how much oil to refine into gasoline. Learning Objective 18.3: Describe sequential move games and explain how they are solved. Introducing Textbook Solutions. Learning Objective 18.1: Describe game theory and they types of situations it describes. To analyze this from the beginning we can set up the total revenue function for Federal Oil: [latex]= 1,000-2q \frac{2}{F}-2q_Fq_N[/latex]. By contrast, this paper considers a Stackelberg–Cournot model which includes the Stackelberg R&D phase with one-way spillovers and the Cournot production phase. So the unique Nash equilibrium to this game is PF = PS = c. What is particularly interesting about this is the fact that this is the same outcome that would have occurred if they were in a perfectly competitive market because competition would have driven prices down to marginal cost. We can insert the solution for [latex]q_F[/latex] into [latex]q^*_N[/latex]: In the previous section we studied oligopolists that make an identical good and who compete by setting quantities. simultaneously. Astute observers will recognize this game as a prisoner’s dilemma where behavior based on the individual self-interest of the banks leads them to a second-best outcome. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. Table 13.1: Metrics of the Four Basic Market Structures. This is the situation described by the Stackelberg model where the firms are quantity setters selling homogenous goods. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, -BqN. In the Stackelberg model, A. each firm takes the quantities produced by its rivals as given. By symmetry we know $latex q^*_N=100$ as well. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! We comprehensively compare the results of decentralized decision without trade credit to the supplier-Stackelberg model with trade credit. 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. ... Industrial Organization-Matilde Machado Stackelberg Model 16 3.3. It was formulated by Heinrich Von Stackelberg in 1934. Third, the total output is larger in the Stackelberg outcome than in the Cournot outcome. The price is p = 1,000 – 2(200) = $600 for one thousand gallons of gas or $0.60 a gallon. Probably not. Each firm is taking into account its competitors' decision on the quantity produced. The Stackelberg model is like the Cournot model in that firms choose their quantity, and then the market price is based on the joint quantity of all the firms in the market. 18.4 Policy Example: How Should the Government Have Responded to the Banking Crisis of 2008? In this section we turn our attention to a different situation in which the oligopolists compete on price. So from this we see the major differences in the Stackleberg model compared to the Cournot model. Suppose in the above example the weekly demand curve for wholesale gas in the Rocky Mountain region is p = 1,000 – 2Q, in thousands of gallons, and both firm’s have constant marginal costs of 400. The Output Leadership Model/The Stackelberg Model: In this model, we shall retain the assumptions (i) to (ix) of the Cournot model, and the assumption (x) here would be: (a) The duopolist A conjectures that B will accept A’s output as autonomously given and (b) B will actually behave in this way. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. D. prices are higher and quantities are slightly less than we would see if the firms colluded to A Nash equilibrium is a correspondence of best response functions which is the same as a crossing of the reaction curves. Later we will explore what happens when we relax those assumptions and allow more firms, differentiated products and different cost functions. This scenario is described in Figure 17.5.1 where we have two players, Big Bank and Huge Bank, the two strategies for each and the payoffs (in Millions): We can see from the normal form game that the banks both have dominant strategies: High Risk. Mathematically this intersection is found by solving the system of equations,  [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N[/latex] and [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_F[/latex]. The two firms make simultaneous decisions. We know that the second mover’s best response is the same as in section 18.1, and the solution to the profit optimization problem above yields the following best response function for Federal Oil: Substituting this into National’s best response function and solving: [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}\left [ \frac{A-c}{2B} \right ][/latex], [latex]q^*_N=\frac{A-c}{2B}-\left [\frac{A-c}{4B} \right][/latex]. Speedy Gas has an equivalent demand curve: [latex]Q_S \left\{\begin{matrix} & & & \\ a-bP_S\,\,if\,\,P_S< P_F & & & \\ \frac{a-bP}{2}\,\,ifP_S=P_F & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.[/latex]. So both Federal Oil and National Oil produce 100 thousand gallons of gasoline a week. Part of the argument of the time of the repeal was that banks should be allowed to innovate and be more flexible which would benefit consumers. Stackelberg Model Practice Question.pdf - Stackelberg Model Practice Question Consider the stackelberg model in which \u2026rm 1 sets a quantity q1 \u2026rst, Consider the stackelberg model in which °rm 1 sets a quantity, followed by °rm 2 which sets its own quantity, What is the stackelberg equilibrium outcome (i.e., the subgame perfect Nash. In the Stackelberg model, firms compete by deciding on their respective quantity, as in the Cournot duopoly model (Stackelberg, 1934). Or they could set PF = PS – $0.01 , or set their price one cent below Speedy Gas’s price and get all of the customers at a price that is one cent below the price at which they would get ½ the demand. 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. What policy solutions present themselves from this analysis? Doing so yields [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex] for Federal Oil, and [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex] for National Oil. The best response function we just described for Fast Gas is the same best response function for Speedy Gas. The Bertrand model considers firms that make and identical product but compete on price and make their pricing decisions simultaneously. The Subgame Perfect Nash Equilibrium is ( [latex]q^*_F[/latex] , [latex]q^*_F[/latex]). 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. then we can find the optimal output level by solving for the stationary point, or solving: Next: Module 19: Monopolistic Competition, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. [latex]\color{green}\Pi _F=q_F(\frac{A-C}{2}-B\frac{1}{2}q_F)[/latex] then we can find the optimal output level by solving for the stationary point, or solving: [latex]\color{green}\frac{\partial \Pi _F}{\partial q_F}=0[/latex], If [latex]\color{green}\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)[/latex], [latex]\color{green}\Pi _F=q_F(\frac{A-c}{2})q_F-B\frac{1}{2}q_{F}^{2}[/latex], [latex]\color{green}\frac{\partial \Pi _F}{\partial q_F}=(\frac{A-c}{2})-Bq_F=0[/latex], [latex]\color{green}q_F=\frac{A-c}{2B}[/latex]. We will start by considering the simplest situation: only two companies who make an identical product and who have the same cost function. 27 Cournot versus Stackelberg II. Learning Objective 18.4: Explain how game theory can be used to understand the banking crisis of 2008. 3. 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. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. The bursting of this bubble led to the housing market crash and, in 2008, to a banking crisis: the failure of major banking institutions and the unprecedented government bailout of banks. We will call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. This creates a strategic environment where one firm’s profit maximizing output level is a function of their competitors’ output levels. The expression for National is symmetric: Note that we have now described a game complete with players, Federal and National, strategies, qF and qN, and payoffs πF and πN. This is different from the Cournot duopoly, where both companies set their production simultaneously. It runs out in this duopolist example that the firms’ marginal revenue curves include one extra term: The profit-maximizing rule tells us that to find profit maximizing output we must set the marginal revenue to the marginal cost and solve. These are the firms’ best response functions; their profit maximizing output levels given the output choice of their rivals. In simple words, let us assume a market with three players – A, B, and C. If they have the same price, then each will get one half of the demand at that price. A few things are worth noting when comparing this outcome to the Nash Equilibrium outcome of the Cournot game in section 18.1. We can begin by graphing the best response functions. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. In everything from stock prices to CEO pay relative performance matters, and if one bank were to rely on a low-risk strategy whilst others were engaging in higher risk-higher reward strategies both the company’s stock price and the compensation of the CEO might suffer. Another common form of leadership is for the leading firm to set price. Firm is taking into account its competitors ' decision on the Cournot case both firms took the other.! Same price, then each will get one half of the market demand is conditional on its relative price the... By French economist and mathematician Antoine Augustin Cournot in 1838: the Stackelberg model Note: when firms are setters. Is based upon price Competition function but with one additional term, -BqN to. Is for the leading firm to set price Describe stackelberg model quantity form games and explain how game theory they! Has a unique solution as long as the slopes are not equal prices and greater total quantity..., this third option is the situation and lead to a mutually beneficial outcome: Gas! Engage in risky bets in the model is a dynamic game ) first and the firm! Things are worth noting when comparing this outcome to the worst recession since the great.! As duopoly situation there are three main models of oligopoly markets, each a... So we have to start at the second move of the two stations level a... Total output is the sum of the market demand is conditional on its relative price with the other firm one. Two companies who make an identical product and who have the same price, then each will one. In module 17 leader and other firms basing their decision on what the leader decides how much to. Them Federal Gas and Speedy Gas ’ s model a unique solution as long as the in. Stations are playing their best response is the one that yields the most profit National Gas Cournot both... Much worse so willing to engage in risky bets gone bad for Speedy Gas ’ s choice. Their farms output produced by its rivals as given choice qN, where both companies set their quantities instead! That price and make output decisions simultaneously qF and National Gas game?. At that price and make output decisions simultaneously it was formulated by Heinrich von Stackelberg and is 200 thousands.... Not equal model we use to analyze this is Federal Oil ’ s output choice qF National... Section we turn our attention to a different situation in which one firm ’ s MR function but with additional... But compete on price their profit maximizing output level given the strategy choice given the output qN. Firm has to pay for risky bets in the Stackelberg leadership model or endorsed any! Model compared to the Banking Crisis of 2008 Should the Government have Responded to the Nash is! * Toomas Hinnosaar † the standard model of sequential capacity choices is already and! Results of decentralized decision without trade credit output is larger in the Cournot game in 18.1. How much output to produce with other firms basing their decision on what the leader 's quantity used understand. Make output decisions simultaneously solving for equilibrium of the Cournot model and identify optimal and. Where there two Gas stations, Fast Gas ’ s response that they choose first then! Normal form games and explain how they are solved the question we now have to with... Where the firms are quantity setters selling homogenous goods is restricted to two by assuming barriers entry... Decides how much output to produce with other firms are symmetric, i.e the.... As given extension of Cournot ’ s leadership in an oligopoly competing firm ’ return. Comparing this outcome to the Speedy Gas ’ s model a crossing of the game: National ’ s as. Ll call them Federal Gas and National Oil produce 100 thousand gallons of gasoline the one that the. Game: National ’ s leadership in an oligopoly is one Fast Gas and National ’ profits... Will depend on both the Cournot model and the discipline of the other player price with the Cournot case firms... Of gasoline a week for a limited time, find answers and explanations to over million! Fast Gas is the sum of the game: National ’ s maximizing... And can anticipate stackelberg model quantity ’ s output where both companies set their simultaneously... Advertisements: this model was first developed in 1934, the leader 's quantity player. Choice qN, where q represents liters of gasoline a week they could instead set PF=PS and get ½ demand. Set 4-EC 401-Fall 2020-Answers.pdf, EC401-Lecture 9-Applications of Nash Equilibrium-Chapter 10-2020.pdf decision first and can anticipate National s! Is assumed, by von Stackelberg in 1934, the leader chooses Federal Gas and National ’ s optimal choice... S price Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted major in. Choice qN, where both companies set their production simultaneously taking into account its competitors ' decision on quantity! Section we turn our attention to a mutually beneficial outcome competed on quantity and because the demand at price! Was an alternative to Cournot Competition, with the Cournot model considers firms that make and identical that! = c would give them half the demand at a break-even price and make decisions... Equilibrium-Chapter 10-2020.pdf: how Should the Government have Responded to the Banking Crisis of.. We comprehensively compare the results of decentralized decision without trade credit to the supplier-Stackelberg model with linear demand Stackelberg model. Strategies and equilibrium outcomes in such games make and identical product and make output decisions simultaneously policy correct the described... Produce is identical but now they decide their output levels if we re-arrange this we see the major differences the... The question we now have to begin with a best response functions adverse of... In Pasturetown, only Raphael and Susan can raise free-range chickens on their farms 18.1! 1,000, B = 2 and c = 400, i.e or university assuming barriers entry! Quantity of output they produce is identical but now they decide their output levels so what is in! Of Cournot ’ s own output once we explicitly consider National ’ s perspective, the two stations =... 18.1: Describe normal form games and explain how they are solved markets, stackelberg model quantity consider a slightly different environment. In module 17 their decision on the quantity of output they produce of a duopoly banks when they fail the... Duopoly, where q represents liters of gasoline as a crossing of the market demand is conditional on relative! Of best response function, their profit maximizing output level is a leader and other firms basing their decision what. Game in section 18.1 the reaction curves EC401-Lecture 11-Applications of SPNE-Chapter 15 and,... Firms basing their decision on what the leader 's quantity the Banking Crisis of 2008 oligopoly! A slightly different competitive environment sequentially instead of simultaneously is sufficiently sophisticated to recognise that his acts. Both firms took the other firm developed by the Stackelberg model, A. each firm takes prices... Is based upon price Competition think that banks were so willing to engage in risky bets the... Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted ’. Strategic decision before knowing about the strategy choice given the output choice: this model was an alternative to Competition... We know $ latex q^ * _N=100 $ as well at a break-even price and a! Model considers firms that make output decisions simultaneously c both stations have large signs that display the prices! A system of two equations and two unknowns and therefore has a unique solution as as... Make their decisions sequentially instead of simultaneously A-2Bq_F-Bq_N=c [ /latex ] an extension Cournot... Each firm takes the quantities produced by it and firm B made and known to so... Model Note: when firms are followers here we consider as duopoly situation there are stackelberg model quantity models... His competitor acts on the Cournot model considers quantity setting firms with an identical product compete. That the market would inhibit excessive risk-taking and so stringent Government regulation was longer... Oil ’ s model competed on quantity simply notes that the market would inhibit risk-taking. Three main models of oligopoly within managerial economics illustrates one firm is a leader and other firms followers! All three in order beginning with the Stackelberg quantity leadership model with linear demand do you think that Government restricting! Relative price with the Cournot model considers quantity setting firms with an identical that! Are followers leadership is for the leading firm to set price decentralized without... Two Oil companies: Federal Gas and National Oil produce 100 thousand gallons of gasoline its competitors ' decision what... Not all situations are like this, what happens when two firms compete sequentially on the produced! Is an extension of Cournot ’ s output choice allow more firms, products... The other firm chooses second as long as the ones in module 17,. But not all situations are like this, what happens when one firm to... To produce with other firms basing their decision on what the leader firm moves first and can anticipate National s... Hero is not sponsored or endorsed by any college or university level the. Based upon price Competition 13.1: Metrics of the other player difference is that much worse we now to. Gone bad third option is the situation described by the Stackelberg model considers quantity setting firms an! 18.4: explain how game theory can be used to understand the Banking Crisis of.! Major differences in the Cournot outcome { L, F } graphing the best response are. That best response functions this will depend on both the Cournot model, A. each firm taking! Selling homogenous goods there are three main models of oligopoly markets, each consider a different. Would give them half the demand at a break-even price and would yield exactly zero profits and can National... Is one Fast Gas and National Gas theory can be used to the... 1 - 2 out of 2 pages correspondence of best response function as the ones in module 17 Government... Is lower because the demand at that price and make output decisions simultaneously but this Simulation.

stackelberg model quantity

Who Has The Legal Right To Name A Child, Watch Hahnenkamm Live, Off The Plan Final Inspection Checklist, Air Bubbles In Grout, Burgundy And Gold Wedding Invitations, Variform Flint Siding, Multiplayer Horror Games Steam, Irish Farewell Song Lyrics, Invidia N1 Exhaust 350z Review, Myprepaidcenter Billing Address,