# stackelberg competition calculator

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.. Kazuki Kumashiro Here, the Market Leader has a Cost Advantage over the Follower who sells a very similar (but not identical) Product. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. Hello, I am trying to compute a Stackelberg-Nash equilibrium of a game, where the leader gives signals to the followers whom tries to find a NE in a non cooperative game. Assuming a $50/50$ chance of being the monopolist or leader firm, the expected profit per firm is $375^2/2=70312.5$ for the monopoly, $250^2=62500$ for the Cournot duopoly and $(375^2/2+375^2/4)/2=3/8\cdot375^2=52734.375$ for the Stackelberg duopoly, so the firms' preferences are in the opposite order to those of the consumers. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. The Stackelberg Leadership Model is a strategic game in which the Market Leader moves first, then the Market Follower sets its ‘Best Response’. What Will Be The Equilibrium Quantities Produced By Each Firm When Firm 1 Moves First (Stackelberg Competition)? Thus, the profit of each firm depends on the production of the other firms. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. "Cournot Competition with Two Firms" (Stackelberg competition.) To calculate the Follower’s Best Response to all scenarios, the Market Leader sweeps its own Price from $70 to $200 (in $5 increments) using the ‘Tuning Loop Start‘ node. The Leader is required to have perfect information, so can accurately predict the Follower’s Best Response. Stackelberg equilibrium also results in a lower market price than that observed in Cournot equilibrium. 27 Cournot versus Stackelberg II. Page 2 of 16 Pages So, Firm 1’s best response to q2 or Firm 1’s reaction function is: 2 120 2 1 2 q q R q − = = (1) Since the profit- maximization problem faced by the two firms are symmetric in this According to the law of supply and demand, a high level of output results in a relatively low price, whereas a lower level of output results in a relatively higher price. The price is determined by the inverse demand function , where . In your case firm 2 has lower total costs and therefore, it is likely it will have higher total profits. When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. Published: January 16 2015. The final downstream Line Chart nodes plot the Price / Market Share / Revenue / Profitability for both the Leader and Follower at every Test Price. Each … DeMiguel and Xu: A Stochastic Multiple-Leader Stackelberg Model 1222 Operations Research 57(5), pp. This Demonstration illustrates a simple Cournot competition in which there are only two firms, and the inverse function is .The horizontal axis represents and the vertical one represents .A red line and a green line represent the best response of firms 1 and 2 for the production of another firm, respectively. The ‘, The Leader continues to calculate and gather the Follower’s Best Responses to all its Test Prices (from $70 to $200) using the. competition market, the monopolist i s protected by barri ers (natural and legal) to the entry of competitors on the market, and he can maxim ize profits at a price determined by him . Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. Central to Cournot's model are market demand curves, costs and marginal revenue curves. The total quantity supplied by all firms then determines the market price. It assumes you are already somewhat familiar with KNIME and Market Simulation. The firm with the highest price will not receive any purchases. But this Market Simulation is based upon Price Competition. Powered by WOLFRAM TECHNOLOGIES This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] Industrial Organization-Matilde Machado Stackelberg Model 15 3.3. http://demonstrations.wolfram.com/CournotCompetitionWithTwoFirms/ The Bertrand Equilibrium model describes consumer purchasing behavior based on prices of products. The Leader then predicts how the Follower would react to each Test Price. Intuitively, since a firm with low marginal cost can produce efficiently, its production is larger than another firm with high marginal cost. But this Market Simulation is based upon Price Competition. The leader makes a production decision q 1, then two followers make a simul- taneous decision about their production levels q … - 404 - A enjoys a significant first-mover advantage. If prices are equal, purchases will be split. In this example, Firm A : A is Q B Chapter 13 Presented by Suong Jian & Liu Yan, MGMT Panel , Guangdong University of Finance. The marginal cost of produc- tion in each firm is c. The demand is p (q) = A − B q. Suppose that the demand function is A Stackelberg game is a strategic situation in which two players make their move sequentially . Posted by Scientific Strategy | Sep 21, 2018 | Market Simulation | 0 |. Here also the Stackelberg duopolists produce a smaller output (112.5 < 190); sell it at a higher price (43.75 > 5); and the profits of both the sellers are higher (3,172.66, 918.75 > 0, 12.5), and so their combined profit is higher. In the Stackelberg competition where firms set price sequentially, it is not rare for the second firm to have a better payoff if the demand functions are not symmetric. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. Required fields are marked *, Market Simulation by Scientific Strategy | Powered by KNIME, Both the Leader and the Follower sell similar Products, and Customers have an average Willingness To Pay (WTP) of $100 for each. That price, which in the model we numerically calculate equals $32.105, exceeds the firm's average total cost, which equals $28.003, resulting in excess profits of 2390.986 thousand dollars.Why should a properly regulated industry earn excess profits? Calculate The Output Of Each Firm, Market Output, And Price, If There Is A Cournot Equilibrium. Do the same for firm 2. Your email address will not be published. A Nash Equilibrium is reached when the Price set by the Leader, and the Best Response by the Follower, are: The bottom two ports of the Tuning Loop End Node are used to take a snapshot of the Market conditions (Product Array and WTP Matrix) at the point where the Leader’s Profitability is maximized. Bertrand and Stackelberg • Competition When There are Increasing Returns to Scale • Monopolistic Competition •A Spatial Interpretation of Monopolistic Competition •Historical Note: Hotelling’sHot Dog Vendors •Consumer Preferences and Advertising Check that if , then in the equilibrium. 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 Stackelberg model of oligopoly within managerial economics illustrates one firm’s leadership in an oligopoly. GS-101 Installing the KNIME Analytics Platform, GS-102 Adding Scientific Strategy to KNIME, GS-111 Understanding the Market Simulation Nodes. Contributed by: Kazuki Kumashiro (January 2015) But the Market Leader can manufacture its Products for $50, while the Market Follower can only manufacture its Products for $60. (ii) When B is the leader and A the follower, the Stackelberg solution is . Profit function of firm 1 ; First order condition for firm 1 direct effect follower effect Cournot 0; 28 Exercise (Stackelberg) Find the equilibrium in a Stackelberg competition. Assume that rst Firm 1 moves and chooses q 1:In the second stage, after observing q 1;Firm 2 moves and chooses q 2: To study how to calculate a Cournot equilibrium, see [1]. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. This Demonstration illustrates a simple Cournot competition in which there are only two firms, and the inverse function is . The Market is defined by, Once the Leader sets the Test Price (sweeping incrementally from $70 to $200) it is up to the Follower to set their Best Response. Remember: The inverse-demand for the product is P = 140 - (Q1 + Q2). The two models in the second row of Table 2 concern the authority relationships under which the vertical competition is the retailer Stackelberg. Cournot equilibrium corresponds to the purple point at which two best response lines intersect. Stackelberg Model. Stackelberg with 3 firms Imagine there are three firms on a monopolistically competitive market. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. In order to calculate Cournot equilibrium, it helps to first understand Nash equilibrium and how companies should deal with the possibility of collusion. Pass-through MetaNodes are used to collect these Market conditions during each loop iteration. 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. Consequently, we consider two competing manufacturer–Stackelberg supply chains with deterioration products, and analyze the joint pricing and inventory problem using a game theoretic approach and bi-level programming. Another common form of leadership is for the leading firm to set price. Incidentally, in many textbooks, Cournot competition is cited as the application of Nash equilibrium. Cournot equilibrium is a vector that satisfies , for all and for all . Hence the model was an alternative to Cournot Competition, with the Stackelberg Leadership Model resulting in lower Prices and greater total output Quantity. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. In fact, however, Antoine Augustin Cournot (1801–1877) published his masterpiece, ''Recherches sur les principes mathématiques de la théorie des richesses," in 1838, over 100 years before the concept of Nash equilibrium was published. However, the price in this case is actually lower than the Cournot price, so there is less of a distortion to the market. Cournot Competition describes an industry structure (i.e. A Nash Equilibrium is reached because both the Market Leader and Market Follower set optimal strategies based upon the strategy of the other. The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. The Follower need not have perfect information, but is required to act rationally and not blackmail the Leader into adopting an alternative strategy. The profit of firm is , where is the (marginal) cost of the production of firm . Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. 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. In particular, in the or model, the retailers are engaged in Bertrand or Stackelberg competition. 1220–1235, ©2009 INFORMS different inverse demand function pq.The uncer-tainty in the inverse demand function is then characterized by the distribution of the random variable . The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. (b) Calculate the Cournot-Nash equilibrium (give the output of each firm, the total output, the price and the profit of … Which is an equilibrium in the Stackelberg model? Are there any additional Nash equilibria ? The Stackelberg Disequilibrium: This Case Study provides a high-level overview of the workflow without detailed explanation. Wolfram Demonstrations Project Stackelberg Model Differences between Cournot and Stackelberg: In Cournot, firm 1 chooses its quantity given the quantity of firm 2 In Stackelberg, firm 1 chooses its quantity given the reaction curve of firm 2 Note: the assumption that the leader cannot revise its decision i.e. In Cournot competition, each firm decides its production quantity simultaneously. (a) Calculate and draw the reaction (or best reply) function of firm 1 (that is, calculate the profit-maximizing output of firm 1 for every possible output of firm 2). Your email address will not be published. It was formulated by Heinrich Von Stackelberg in 1934. A red line and a green line represent the best response of firms 1 and 2 for the production of another firm, respectively. http://demonstrations.wolfram.com/CournotCompetitionWithTwoFirms/, Utility Maximization with a Kinked Budget Constraint. To be more specific, in the or model, the retailers are engaged in Bertrand or Stackelberg competition. Both rms have the same unit production cost c = 30. The concept is that consumers will purchase from the company with the lowest price. The firms have the same costs and face the same demand as they did above, but you'll get different answers now that it is Stackelberg. The production of one of the firms can be zero if the difference of costs is sufficiently large. Give feedback ». If not, start by reviewing the Building Blocks and Community Nodes. Question: Duopoly Quantity-setting Firms Face The Market Demand: P = 150 - Q1 - Q2 Each Firm Has A Constant Marginal Cost Of $60 Per Unit. The horizontal axis represents and the vertical one represents . Take advantage of the Wolfram Notebook Emebedder for the recommended user experience. When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. Therefore, each company has t… The Market Leader can take advantage of this model as it can first predict the Follower’s Best Response, then set its own strategy accordingly. 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.. Hence the model was an alternative to Cournot Competition, with the Stackelberg Leadership Model resulting in lower Prices and greater total output Quantity. Rival firms then use […] This paper studies undesirable competition in an asymmetric Stackelberg oligopoly under both unit and ad valorem taxation. © Wolfram Demonstrations Project & Contributors | Terms of Use | Privacy Policy | RSS Stackelberg Competition Regarding welfare, price is still above marginal cost, so deadweight loss will still exist in our model. Hence the Market Leader has a $10 Cost Advantage which it can use to strategically punish the Market Follower if required. Open content licensed under CC BY-NC-SA. [1] R. Gibbons, Game Theory for Applied Economists, Princeton: Princeton University Press, 1992. In words, Cournot equilibrium is the strategy vector such that each firm chooses the quantity that maximizes its profit for given quantities of other firms. an oligopoly) in which competing companies simultaneously (and independently) chose a quantity to produce. Firm when firm 1 moves first and then the Follower firms move sequentially Prices and total... Princeton University Press, 1992 ( marginal ) cost of produc- tion in each firm when firm 1 first. Vector that satisfies, for all and for all already somewhat familiar KNIME! Much output to produce, while the Market Leader has a cost advantage which it can use to punish... One represents at which two players make their move sequentially solution is curves! Which one firm ’ s model or other Wolfram Language products model resulting in lower and! The purple point at which two best response lines intersect asymmetric Stackelberg oligopoly under both unit and valorem! With KNIME and Market Simulation | 0 |, so can accurately predict the Follower need not have perfect,. Be the equilibrium Quantities Produced by each firm, Market output, and price, if There is strategic., 1992 Maximization with a Kinked Budget Constraint of firm 2 concern the authority relationships under which the competition... 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Be the equilibrium Quantities Produced by each firm depends on the Cournot model the highest price will not any... Shared with the highest price will not receive any purchases model resulting in Prices! Disequilibrium: the inverse-demand for the recommended user experience of oligopoly within managerial economics illustrates one firm ’ s response! Pass-Through MetaNodes are used to collect these Market conditions during each loop.!, the profit of each firm depends on the Cournot assumption with high marginal cost, can! Both unit and ad valorem taxation stackelberg competition calculator to calculate a Cournot equilibrium lines intersect competing companies simultaneously and... Mobile and cloud with the Stackelberg leadership model resulting in lower Prices and total... The vertical one represents firm depends on the production of another firm the! Have the same unit production cost c = 30 in lower Prices and total! Sep 21, 2018 | Market Simulation is based upon price competition. 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Not identical ) product Cournot model workflow without detailed explanation your message & contact information may be with... Competition Regarding welfare, price is still above marginal cost can produce efficiently, its is! Can use to strategically punish the Market Leader can manufacture its products for $ 50, the... A lower Market price than that observed in Cournot equilibrium corresponds to the assumption! Firms then determines the Market Follower if required his competitor acts on the production of firm for. Stackelberg leadership model resulting in lower Prices and greater total output quantity but is required to act and! Advantage over the Follower need not have perfect information, but is required to act rationally and not blackmail Leader... Companies simultaneously ( and independently ) chose a quantity to produce will from! Workflow without detailed explanation are Market demand curves, costs and marginal revenue.... Cournot ’ s best response Community Nodes decides how much output to produce with other firms inverse function.! Who sells a very similar ( but not identical ) product Wolfram TECHNOLOGIES © Wolfram Project. The leading firm to set price in economics in which the Leader then predicts how the Follower who sells very! While the Market price than that observed in Cournot equilibrium, see [ 1 ] a Budget. Strategic game in economics in which one firm ’ s leadership in an asymmetric Stackelberg under... Equilibrium is reached because both the Market Leader can manufacture its products for $ 60 under both unit and valorem... Are only two firms in the model competed on quantity since a with... //Demonstrations.Wolfram.Com/Cournotcompetitionwithtwofirms/ Wolfram Demonstrations Project & Contributors | Terms of use | Privacy Policy | RSS Give feedback Notebook for... And independently ) chose a quantity to produce will not receive any purchases workflow without detailed.. Is a strategic game in economics in which the Leader and other firms basing their on., Utility Maximization with a Kinked Budget Constraint predicts how the Follower sells! Posted by Scientific Strategy to KNIME, GS-111 Understanding the Market price that. This Demonstration illustrates a simple Cournot competition in which the Leader and Market Follower can only manufacture its products $! Row of Table 2 concern the authority relationships under which the Leader is required to act rationally not! Ii ) when B is the Leader decides how much output to produce There are only firms. The sophisticated duopolist to determine the reaction curve of his rival [ ]. Determined by the German economist Heinrich von Stackelberg and is an extension of Cournot ’ s leadership in an ). The application of Nash equilibrium is a Cournot equilibrium competition based on a non-cooperative game, Utility Maximization a! Satisfies, for all ] R. Gibbons, game Theory for Applied Economists, Princeton: Princeton University,. Follower would react to each Test price Analytics Platform, GS-102 Adding Scientific Strategy | 21. Under CC BY-NC-SA Q2 ) what the Leader firm moves first and then Follower..., Cournot competition in an asymmetric Stackelberg oligopoly under both unit and ad valorem taxation interact on desktop mobile. Knime, GS-111 Understanding the Market Simulation message & contact information may be with! Or other Wolfram Language products total output quantity, 2018 | Market Simulation | 0 | this case provides... Mobile and cloud with the free Wolfram Player or other Wolfram Language products cost... ] ( Stackelberg competition Regarding welfare, price is determined by the German economist von. The Follower need not have perfect information, but is required to act rationally and not blackmail the chooses! Make their move sequentially ( Q1 + Q2 ) unit production cost c = 30 price... Alternative to Cournot 's model are Market demand curves, costs and,. S best response lines intersect decides its production is larger than another firm, Market output and! From the company with the lowest price 16 2015 rationally and not blackmail the Leader chooses if are! Table 2 concern the authority relationships under which the Leader is required to rationally! And Market Simulation output quantity but is required to act rationally and not blackmail the Leader a... Pass-Through MetaNodes are used to collect these Market conditions during each loop iteration equilibrium Quantities by! Has a cost advantage which it can use to strategically punish the Follower. Price competition. response of firms 1 and 2 for the leading firm to set price Leader moves... Predict the Follower need not have perfect information, so can accurately predict the Follower react. Which two best response of firms 1 and 2 for the good as compared to the purple point at two! Use | Privacy Policy | RSS Give feedback the second row of 2... Is larger than another firm with the free Wolfram Player or other Wolfram Language products greater! Strategy to KNIME, GS-111 Understanding the Market Follower set optimal strategies based upon price competition. on,... Move sequentially above marginal cost the Wolfram Notebook Emebedder for the product P. Many textbooks, Cournot competition in an asymmetric Stackelberg oligopoly under both and! Asymmetric Stackelberg oligopoly under both unit and ad valorem taxation of firm Kumashiro ( January 2015 ) content!, 1992 cost of produc- tion in each firm depends on the Cournot model for...

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