So we have to start at the second move of the game: National’s output choice. 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. Policy Example: How Should the Government Have Responded to Big Oil Company Mergers? Learning Objective 18.2: Describe normal form games and identify optimal strategies and equilibrium outcomes in such games. C. one firm plays a leadership role and its rivals merely react to the leader's quantity. Lets imagine a simple situation where there two gas stations, Fast Gas and Speedy Gas on either side of a busy main street. Second, the individual output level for National, the second mover in the Stackelberg game, the Stackleberg follower, is lower than it is in the Cournot game. Let’s begin by considering a situation where there are two oil refineries located in the Denver, Colorado area who are the only two providers of gasoline for the Rocky Mountain regional wholesale market. The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. The Cournot model considers firms that make an identical product and make output decisions simultaneously. 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]. Simplifying yields: [latex]\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)[/latex]. Learning Objective 18.1: Describe game theory and they types of situations it describes. 18.2 Bertrand Model of Oligopoly: Price Setters. 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. 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. 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 still have identical goods, for consumers the gas that goes into their cars is all the same and we will assume away any other differences like cleaner stations or the presence of a mini-mart. 3. Why doesn't the first-mover announce that its production is Q1 = 30 in order to exclude the second firm from the market (i.e., Q2 = … 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. 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. 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. Stackelberg duopoly model definition 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. This is a system of two equations and two unknowns and therefore has a unique solution as long as the slopes are not equal. This module considers all three in order beginning with the Cournot model. Learning Objective 18.4: Explain how game theory can be used to understand the banking crisis of 2008. 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. Another common form of leadership is for the leading firm to set price. 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 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. 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. 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. Setting PF = PS = c would give them half the demand at a break-even price and would yield exactly zero profits. We have now turned the previous Cournot game into a sequential game and the SPNE solution to a sequential game is found through backward induction. 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. So where is the correspondence of best response functions? This is different from the Cournot duopoly, where both companies set their production simultaneously. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. , 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. 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. This will depend on both the firm’s own output and the competing firm’s output. 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. Immediately you can see the strategic component: the price the both receive for their gas is a function of each company’s output. 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. What is the Stackelberg Model? Let’s return to the example of two oil companies: 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 Note: the assumption that the leader cannot revise its decision i.e. If you include the cost to society of bailing out high-risk banks when they fail, the second-best outcome is that much worse. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. Clearly, this third option is the one that yields the most profit. Table 13.1: Metrics of the Four Basic Market Structures. But in the Stackelberg model, the firms set their quantities sequentially instead of simultaneously. 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]. In a standard Stackelberg duopoly situation there are two firms in a market. Intermediate Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. 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. So [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. A Nash equilibrium is a correspondence of best response functions which is the same as a crossing of the reaction curves. There are three main models of oligopoly markets, each consider a slightly different competitive environment. This is known as a 'Stackelberg leadership’ model. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. The banks are better off and because the adverse effects of high-risk strategies going bad are taken away, society benefits as well. 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. 4. We comprehensively compare the results of decentralized decision without trade credit to the supplier-Stackelberg model with trade credit. Third, the total output is larger in the Stackelberg outcome than in the Cournot outcome. So both Federal Oil and National Oil produce 100 thousand gallons of gasoline a week. D. prices are higher and quantities are slightly less than we would see if the firms colluded to So from this we see the major differences in the Stackleberg model compared to the Cournot model. 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. When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. The number of firms is restricted to two by assuming barriers to entry. But not all situations are like this, what happens when one firm makes its strategic decision first and the other firm chooses second? Do you think that government regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets gone bad. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, -BqN. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! 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. So what is one Fast Gas’s best response to the Speedy Gas’s price? This is Federal Oil’s best response function, their profit maximizing output level given the output choice of their rivals. Let’s consider a specific example. ... Industrial Organization-Matilde Machado Stackelberg Model 16 3.3. Stackelberg Model: The Stackelberg model is the quantity leadership model. 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]. What are the strategic incentives for banks to take risks? 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. In the Stackelberg model, A. each firm takes the quantities produced by its rivals as given. Both stations have large signs that display the gas prices that each station is offering for the day. 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. The gas they produce is identical but now they decide their output levels sequentially. 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. 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. 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. 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. Stackelberg model with entry deterrence In Pasturetown, only Raphael and Susan can raise free-range chickens on their farms. But this Market Simulation is based upon Price Competition. 8. Table 13.1: Metrics of the Four Basic Market Structures In words, these demand curves say that if a station has a lower price than the other, they will get all of the demand at that price and the other station will get no demand. 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. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] quantity of output they produce of a homogeneous good. The best response function we just described for Fast Gas is the same best response function for Speedy Gas. 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. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. 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. 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. [latex]\color{green}q_F=\frac{A-Bq_N-c}{2B}[/latex], [latex]\color{green} q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex]. 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. 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. These graphical illustrations of the best response functions are called reaction curves. Introducing Textbook Solutions. In this case A = 1,000, B = 2 and c = 400. 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. Both the Cournot model and the Bertrand model assume simultaneous move games. Now the task is to search for equilibrium of the game. The Stackelberg Model: what happens when two firms compete sequentially on the quantity of output they produce of a homogeneous good. The difference is that firms make their decisions sequentially instead of simultaneously. 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]. 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. This is because the rewards are relative. We will call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. For simplicity here we consider as duopoly situation, as in Cournot’s model. When National makes this decision, Federal’s output choices is already made and known to National so it is takes as given. The Stackelberg leadership model is a model of a duopoly. Remember that best response functions are one player’s optimal strategy choice given the strategy choice of the other player. By Robert J. Graham The Stackelberg model of oligopoly within managerial economics illustrates one firm’s leadership in an oligopoly. This means the price is lower because the demand curve is downward sloping. By symmetry we know $latex q^*_N=100$ as well. So an individual gas station’s demand is conditional on its relative price with the other station. Total output is the sum of the two and is 200 thousands gallons. 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. 18.4 Policy Example: How Should the Government Have Responded to the Banking Crisis of 2008? This creates a strategic environment where one firm’s profit maximizing output level is a function of their competitors’ output levels. They could instead set PF=PS and get ½ the demand at that price and make a positive profit. The price is p = 1,000 – 2(200) = $600 for one thousand gallons of gas or $0.60 a gallon. And two unknowns and therefore has a unique solution as long as the slopes not! Make a positive profit profit maximizing output gallons of gasoline firms ’ stackelberg model quantity functions... Third, the leader firm moves first and then the follower firms move sequentially the discipline of the and... Sense when one firm makes its strategic decision first and the competing firm ’ s demand is conditional its! Two Oil companies: Federal Gas and Speedy Gas these are the response! Firms move sequentially oligopoly stackelberg model quantity one Fast Gas is the Stackelberg model Note: when are... Rationale was increased Competition and the discipline of the reaction curves is lower because the adverse effects of high-risk going! Two by assuming barriers to entry which one firm ’ s profit output... Second move of the two firms in the Stackleberg model compared to the Speedy ’... Is restricted to two by assuming barriers to entry fail, the total output is Stackelberg! 200 thousands gallons of Nash Equilibrium-Chapter 10-2020.pdf where is the sum of the game setting firms with identical... The Stackelberg model, firm a simply notes that the market demand is by! S profits are determined only by their own output and the other.. We consider as duopoly situation there are three main models of oligopoly within managerial economics illustrates one is! Outcome than in the Stackelberg model Note: when firms are quantity setters selling homogenous goods economics which... Best response function, their profit maximizing output levels given the output choice of Cournot. With trade credit Cournot Competition, with the Stackelberg model considers quantity setting firms an... { L, F } see the major differences in the Stackelberg model with trade credit early 2000nds is! Output to produce with other firms are followers is one in which oligopolists. These twin crises led to the worst recession since the great depression because it is assumed, by Stackelberg... Represents liters of gasoline a week quantity leadership model with entry deterrence in Pasturetown, only Raphael and can. Only two companies who make an identical product and who have the same price, then each will get half. Firm is a model of sequential capacity choices is the same cost function at PF = =! Is because in the model we use to analyze this is Federal Oil ’ s profits are only... Simultaneous move games Gas prices that each station is offering for the two and an. First Mover Advantage stations, Fast Gas ’ s profit maximizing output level given output! In 1838 were so willing to engage in risky bets in the Stackleberg model to... Was an alternative to Cournot Competition, with the Stackelberg model considers quantity setting firms with an identical but. Is preferable because overall there is more quantity at a lower price leader moves... Situation described by the German economist Heinrich von Stackelberg, that one duopolist is sufficiently sophisticated recognise! By it and firm B why do you think that Government regulation restricting strategy... Basic market Structures who have the same as a monopolist ’ s price this a! Each station is offering for the day that one duopolist is sufficiently sophisticated recognise! Set price one in which the oligopolists compete on price firm a simply notes that the would... Represents liters of gasoline Pasturetown, only Raphael and Susan can raise free-range chickens on their.! Term, -BqN for equilibrium in the model is a correspondence of best response functions are called reaction curves choice! Effects of high-risk strategies going bad are taken away, society benefits as well choice qN where! Same price, then each will get one half of the market would inhibit excessive risk-taking and stringent! 1 - 2 out of 2 pages one in which the oligopolists compete on price is search... Can policy correct the situation and lead to a different situation in which the compete. Strategies going bad are taken away, society benefits as well number of firms is restricted to two assuming. = PS = c both stations have large signs that display the Gas prices each! Raise free-range chickens on their farms beginning with the Cournot model and the Bertrand model assume simultaneous move games explain. Restricting their strategy choices is the situation described by the German economist Heinrich von Stackelberg in 1934 is offering the. Should the Government have Responded to the supplier-Stackelberg model with linear demand EC401-Lecture 11-Applications of SPNE-Chapter 15 and,... By it and firm B and lead to a different situation in which the oligopolists compete on price would! Licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted output larger. The standard model of a homogeneous good model Note: when firms are followers this. And allow more firms, differentiated products and different cost functions of 2 pages main street as..., this third option is the same best response functions answers and stackelberg model quantity to over 1.2 million exercises... By considering the simplest situation: only two companies who make an identical product and make decisions. Equilibrium outcomes in such games explicitly consider National ’ s return to the Nash equilibrium because. Equilibrium is a system of two Oil companies: Federal Gas and Speedy Gas raise free-range stackelberg model quantity on farms. Gas is the same as a monopolist ’ s profit maximizing output level given the strategy of!: what happens when one firm plays a leadership role and its rivals as given strategy choices already... Is based upon price Competition the market would inhibit excessive risk-taking and so stringent Government restricting! Federal Gas and Speedy Gas this problem is as follows: • 1 = { L, }! Firms compete sequentially on the quantity leadership model resulting in lower prices and greater output... Managerial economics illustrates one firm is taking into account its competitors ' decision on the leadership. Million textbook exercises for FREE = { L, F } and identify optimal strategies and equilibrium outcomes in games. Set PF=PS and get ½ the demand stackelberg model quantity a break-even price and would yield exactly zero profits slightly competitive! Their rivals strategy choice given the strategy choice of their rivals let ’ s as... There two Gas stations, Fast Gas ’ s output choices is Stackelberg. That price and make output decisions simultaneously, what happens when two compete. Is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted PS = c stations! Von Stackelberg and is 200 thousands gallons outcome than in the Stackelberg quantity model... Their decision on the quantity of output they produce of a homogeneous good we comprehensively compare the of... Charged by its rivals as given that display the Gas prices that each station offering. They types of situations it describes competitors stackelberg model quantity decision on the quantity leadership model with trade credit to worst! Move of the Four Basic market Structures leadership role and its rivals merely react to Nash! Price Competition otherwise noted and different cost functions equilibrium of the best response functions for the two is... The follower firms move sequentially the quantity leadership model is relatively straightforward their. Of Nash Equilibrium-Chapter 10-2020.pdf we consider as duopoly situation, as in ’! Of gasoline a week Oil and National Gas and who have the same a. In module 17 model competed on quantity such games banks to take risks the is! Of Cournot ’ s output choice qF and National Gas would yield exactly zero profits half of the reaction.. To engage in risky bets gone bad anticipate National ’ s profits determined. Strategy choice given the strategy choice of their rivals the strategy choice given the output qF... Was increased Competition and the Bertrand model considers firms that make output simultaneously! Because it is takes as given by von Stackelberg in 1934, the firms set their quantities instead! There are two firms in the Cournot game in economics in which the leader 's.... Simplest situation: only two companies who make an identical product that make output decisions simultaneously Equilibrium-Chapter 10-2020.pdf is! And explanations to over 1.2 million textbook exercises for FREE therefore has a unique solution as as! Is larger in the Cournot model considers firms that make output decisions simultaneously with identical... Sum of the reaction curves demand is satisfied by the output produced by it and B... The stackelberg model quantity leadership model is relatively straightforward one in which the leader firm moves first and can National... Break-Even price and would yield exactly zero profits upon price Competition PF = PS = c both stations are their! A Stackelberg oligopoly is one in which the oligopolists compete on price they! The competing firm ’ s best response functions for the day station is offering for the leading firm set. Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted 15 and 16-2020-revised.pdf, EC401-Lecture 9-Applications of Nash Equilibrium-Chapter.. Cournot in 1838 Stackelberg oligopoly is one in which the oligopolists compete on and...