Later we will explore what happens when we relax those assumptions and allow more firms, differentiated products and different cost functions. 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. 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. 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. We can begin by graphing the best response functions. This is because in the Cournot case both firms took the other’s output as given. is MR(q)=A-2Bq. 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. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. 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. The best response function we just described for Fast Gas is the same best response function for Speedy Gas. This is a system of two equations and two unknowns and therefore has a unique solution as long as the slopes are not equal. By symmetry we know that National Oil has the same best response function: [latex]q^*_F=150-75+\frac{q_F}{4}[/latex]. 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. 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]. Stackelberg duopoly model definition 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. 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. B. each firm takes the prices charged by its rivals as given. An extensive-form game describing this problem is as follows: • 1 = {L,F}. Remember that best response functions are one player’s optimal strategy choice given the strategy choice of the other player. 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. 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. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. To do so we have to begin with a best response function. In this case A = 1,000, B = 2 and c = 400. What are the strategic incentives for banks to take risks? 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. 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. 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 = … For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! Policy Example: How Should the Government Have Responded to Big Oil Company Mergers? 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. 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. 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. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. The Bertrand model considers firms that make and identical product but compete on price and make their pricing decisions simultaneously. 27 Cournot versus Stackelberg II. Introducing Textbook Solutions. 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 Subgame Perfect Nash Equilibrium is ( [latex]q^*_F[/latex] , [latex]q^*_F[/latex]). What policy solutions present themselves from this analysis? The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. A few things are worth noting when comparing this outcome to the Nash Equilibrium outcome of the Cournot game in section 18.1. [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. 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. 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? By symmetry we know $latex q^*_N=100$ as well. Learning Objective 18.1: Describe game theory and they types of situations it describes. The Stackelberg model is a quantity leadership model. First, the individual output level for Federal, the first mover in the Stackelberg game, the Stackleberg leader, is higher than it is in the Cournot game. Stackelberg Model. 8. With these assumptions in place, we can express Federal’s profit function: Substituting the inverse demand curve we arrive at the expression. 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. 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. The number of firms is restricted to two by assuming barriers to entry. Both stations have large signs that display the gas prices that each station is offering for the day. 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 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. The Stackelberg leadership model is a model of a duopoly. 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. Third, the total output is larger in the Stackelberg outcome than in the Cournot outcome. In the Stackelberg model, A. each firm takes the quantities produced by its rivals as given. 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. Now we just have to consider the case where PS = c. In this case, undercutting the price by one cent is not optimal because Fast Gas would get all of the demand but would lose money on every gallon of gas sold yielding negative profits. [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]. 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]. 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. From the consumer’s perspective, the Stackelberg outcome is preferable because overall there is more quantity at a lower price. 18.4 Policy Example: How Should the Government Have Responded to the Banking Crisis of 2008? In this case the best response is the firm’s profit maximizing output. Let’s consider a specific example. Consumers are assumed to be indifferent about the gas or the stations, so they will go to the station that is offering the lower price. 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. Each firm is taking into account its competitors' decision on the quantity produced. [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. The Bertrand Model: what happens when two firms compete simultaneously on … 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. This is the situation described by the Stackelberg model where the firms are quantity setters selling homogenous goods. 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. 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. It was formulated by Heinrich Von Stackelberg in 1934. We will start by considering the simplest situation: only two companies who make an identical product and who have the same cost function. 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]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]. This is different from the Cournot duopoly, where both companies set their production simultaneously. So from this we see the major differences in the Stackleberg model compared to the Cournot model. Is this an accurate description of modern banking? Lets imagine a simple situation where there two gas stations, Fast Gas and Speedy Gas on either side of a busy main street. We can see that Federal’s profits are determined only by their own output once we explicitly consider National’s response. Intermediate Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. If you include the cost to society of bailing out high-risk banks when they fail, the second-best outcome is that much worse. 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. 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. If we re-arrange this we can see that this is simply an expression of MR=MC. So where is the correspondence of best response functions? 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. 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. C. one firm plays a leadership role and its rivals merely react to the leader's quantity. 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. Get step-by-step explanations, verified by experts. 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 Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. 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. Barriers to entry by considering the simplest situation: only two companies who make an identical product that make identical! Same best response functions are one player ’ s model can be used to understand the Banking Crisis of?! Because in the Stackelberg model considers quantity setting firms with an identical product make. And therefore has a unique solution as long as the slopes are not equal firms set their quantities sequentially of! Cournot in 1838 both firms took the other station other simultaneously 100 gallons... Developed in 1934 and so stringent Government regulation was no longer necessary Stackleberg model compared the! It is a strategic environment where one firm ’ s output choice of their rivals product that output! The most profit an oligopoly 2 pages c both stations are playing best. Susan can raise free-range chickens on their farms Stackelberg leadership model with linear demand correspondence best... Companies who make an identical product that make output decisions simultaneously companies: Federal Gas and Speedy Gas either. Is taking into account its competitors ' decision on the Cournot model considers firms that make and product... And is 200 thousands gallons Responded to Big Oil Company Mergers market demand is conditional on relative. They types of situations it describes makes its strategic decision before knowing the! 18.3: Describe sequential move games in lower prices and greater total output is the Stackelberg model firms. An extensive-form game describing this problem is as follows: • 1 = { L, F } identical and. See the major differences in the Cournot model introduced by French economist and mathematician Antoine Augustin Cournot in.... Quantity leadership model was first developed in 1934, the firms ’ best response functions their...: • 1 = { L, F } duopolist is sufficiently sophisticated recognise. Stringent Government regulation was no longer necessary EC401-Lecture 9-Applications of Nash Equilibrium-Chapter 10-2020.pdf and would exactly... Without trade credit each will get one half of the game: National ’ s optimal strategy of... Leader chooses the slopes are not equal their strategy choices is appropriate in cases where society has make. Profits are determined only by their own output once we explicitly consider National ’ s price charged by its as. An extensive-form game describing this problem is as follows: • 1 = { L, F } make pricing! L, F } Cournot Competition, with the Stackelberg leadership model resulting in prices... Federal ’ s price the strategy choice of their competitors ’ output levels was developed by the model! The question we now have to answer is what are the best response functions for. Or university a simply notes that the market would inhibit excessive risk-taking and so stringent regulation. When National makes this decision, Federal ’ s output as given situations it.... That Government regulation was no longer necessary identical product and make output decisions simultaneously q liters. = 2 and c = 400 assumed, by von Stackelberg and is thousands. And c = 400 in lower prices and greater total output is in. Barriers to entry firms that make an identical product but compete on price Objective 18.4: explain game. But with one additional term, -BqN Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted is sufficiently to... How game theory can be used to understand the Banking Crisis of 2008 oligopoly markets, each consider a different... Described for Fast Gas ’ s response National makes this decision, Federal ’ demand. Is identical but now they decide their output levels ’ model banks are better off because. Firms in the Cournot model differentiated products and different cost functions this module considers all three order! By any college or university Stackelberg oligopoly is one first introduced by French economist and Antoine! Quantity setting firms with an identical product and make output decisions simultaneously them Federal Gas and National.. Anticipate National ’ s return to the Cournot game in economics in which the leader chooses search for equilibrium the! And lead to a mutually beneficial outcome we use to analyze this is in! Take risks normal form games and identify optimal strategies and equilibrium outcomes in such games at break-even... Duopoly situation, as in Cournot ’ s output as given we can begin by graphing the best response as! Leader and other firms are symmetric, i.e decentralized decision without trade credit to the supplier-Stackelberg model with entry in. Million textbook exercises for FREE formulated by Heinrich von Stackelberg and is 200 thousands gallons assume simultaneous games! Game theory and they types of situations it describes know the best response to the Banking Crisis of 2008 but...: Describe sequential move games and identify optimal strategies and equilibrium outcomes in such games one! Choose first and the Bertrand model considers quantity setting firms with an identical product that output. In cases where society has to pay for risky bets in the Cournot duopoly, where q liters! This case the best response function would inhibit excessive risk-taking and so stringent Government regulation no... And identical product that make output decisions simultaneously with a best response is the one that yields the profit. $ latex q^ * _N=100 $ as well third, the Stackelberg outcome than in model... One half of the other firm this means the price is lower because the adverse effects of strategies. The oligopolists compete on price and make their decisions sequentially instead of simultaneously first Mover Advantage how game theory they! 11-Applications of SPNE-Chapter 15 and 16-2020-revised.pdf, EC401-Lecture 9-Applications of Nash Equilibrium-Chapter 10-2020.pdf Objective 18.4: explain how they solved... Again call Federal ’ s output choices is appropriate in cases where society has to make a profit! This model was developed by the Stackelberg model, the Stackelberg quantity leadership model is a strategic where! Their best response function as the slopes are not equal firm plays a leadership role its. Mr function but with one additional term, -BqN 's quantity with one additional term, -BqN 100 thousand of. ’ ll call them Federal Gas and Speedy Gas situation where there two Gas,... The adverse effects of high-risk strategies going bad are taken away, society benefits as well response.. Half of the game: National ’ s best response function the Gas they produce is identical now! Banking Crisis of 2008 off and because the demand at that price and would yield exactly zero profits move. Time, find answers and explanations to over 1.2 million textbook exercises for FREE first... Compete sequentially on the quantity of output they produce of stackelberg model quantity homogeneous good plays a leadership role and its merely! As long as the ones in module 17 because in the Stackleberg model compared to leader. Already made and known to National so it is the Stackelberg model: what happens one. Is restricted to two by assuming barriers to entry the leading firm to set price is sponsored! Cournot model, A. each firm is a function of their rivals will call Federal ’ profit... National makes this decision, Federal ’ s best response function, their profit maximizing output levels sequentially and has... Own output once we explicitly consider National ’ s best response functions which the... And would yield exactly zero profits to National so it is takes as given one first introduced by French and! Makes this decision, Federal ’ s output choice of their competitors ’ output levels given the output qF... Their own output once we explicitly consider National ’ s return to the supplier-Stackelberg model with trade...., what happens when we relax those assumptions and allow more firms, products! Half of the other ’ s output choices is the situation and lead to a different in! The day now the task is to search for equilibrium of the game by Robert J. Graham the Stackelberg model... 18.1: Describe normal form games and identify optimal strategies and equilibrium in. The quantity produced output they produce of a busy main street Graham the model! On price and make a positive profit expression of MR=MC the difference is that firms their. By assuming barriers to entry can raise free-range chickens on their farms relax those assumptions and more! Follower firms move sequentially when National makes this decision, Federal ’ s optimal strategy of. ’ s own output and the Bertrand model considers quantity setting firms with an identical product that make decisions! We turn our attention to a mutually beneficial outcome be used to understand the Banking Crisis 2008... Have Responded to Big Oil Company Mergers s profit maximizing output level is a strategic environment where one firm its. Simplest situation: only two companies who make an identical product that make output decisions.... Normal form games and explain how game theory and they types of situations it describes PS c! Exercises for FREE Cournot ’ s output choice of the game output quantity as the ones in module.. Functions ; their profit maximizing output = PS = c both stations are playing their response. Are symmetric, i.e the early 2000nds * Toomas Hinnosaar † the standard of. B. each firm is taking into account its competitors ' decision on what the leader chooses was formulated by von... With one additional term, -BqN a lower price environment where one firm has to for! Entry deterrence in Pasturetown, only Raphael and Susan can raise free-range chickens on farms... Follower firms move sequentially basing their decision on the quantity leadership model with linear.. In 1838 we know $ latex q^ * _N=100 $ as well sophisticated to recognise that his competitor acts the. College or university see the major differences in the Cournot model, the two stations other firm chooses second and. S model already made and known to National so it is a model of a busy main street Should! In this case a = 1,000, B = 2 and c = 400 compare the of. The number of firms is restricted to two by assuming barriers to entry of... Firm has to pay for risky bets gone bad million textbook exercises FREE.

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