Therefore, i = q i 0 @a b Xn j=1 q j 1 A cq i = q i 0 @a c b Xn j=1 q j 1 A: 11/24 A Linear Example with n FirmsII Solving the model: Our model extends Sherali’s deterministic multiple-leader model (Sherali 1984) because it considers the case where Report the best chromosome as the optimal solution. The Cournot and Stackelberg models have been widely studied in the literature. How to Lead Your Competitors: The Stackelberg Model of Duopolies in Managerial Economics. The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. Derive the Stackelberg solution with the following steps: Firms A and B provide the entire market quantity demand, QD. 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.. The market demand curve now faced by the Stackelberg duopolies is: where QD is the market quantity demanded and P is the market price in dollars. This is the major contribution of the paper. For this purpose was used a model of Stackelberg duopoly. What is the Stackelberg Model? Finally, the model credibility examined by using a numerical example to show benefits of the proposed formulation. The simultaneous decision-making associated with the Cournot model leads to different outcomes from the outcomes associated with sequential decisions of the Stackelberg model. endobj Example Model. In Section 5, we present a numerical example and sensitivity analysis, and we propose important conclusions on managerial phenomena. /ProcSet [ /PDF ] endobj The two countries are considering policies to open or close their import markets. stream endobj Substituting one equation in the other we obtain y 1 = (120 (120 y 1 )/4)/4, so that y 1 = 24; substituting in the equation for y 2 we get y 2 = 24. stream stream study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. Therefore, i = q i 0 @a b Xn j=1 q j 1 A cq i = q i 0 @a c b Xn j=1 q j 1 A: 11/24 A Linear Example with n FirmsII Solving the model: For the next step, the demand curve faced by firm A is. Firm A’s total revenue, TRA, equals price times quantity. What are the firms' outputs in a Nash equilibrium of Cournot's model? It was formulated by Heinrich Von Stackelberg in 1934. Assume two firms, where Firm One is the leader and produces Q1 units of a homogeneous good. This is the major contribution of the paper. /Resources 20 0 R If there are two gas stations in the same route, since gas is a homogenous good, the driver will stop at the cheapest one. For price, substitute the equation from Step 2. /FormType 1 >> Assume that firm A has a constant marginal cost of $20 and firm B has a constant marginal cost of $34. x���P(�� �� Thus, the profit-maximizing Stackelberg duopoly has firm A producing 114 units of output and firm B producing 29 units of output. /Filter /FlateDecode Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. On the other hand, firm A doesn’t have a reaction function. 6. Most textbooks present an adequate explanation of the model. /Resources 13 0 R /Subtype /Form In section 4, we apply a numerical example to simulate the model … the numerical examples and analysis are presented. Cournot, Stackelberg, and Monopoly, combined with a fixed-time control policy based on the Webster method, were chosen as benchmarks in a numerical example to test model validity. The market demand of their product is given as P= 30-Q with Q=Q1+Q2, and MC= 12, Find Stackelberg … Numerical example Contract decision models including quantity discount model and the Stackelberg game theoretic model are studied. the numerical examples and analysis are presented. Note that firm B has exactly the same reaction function as existed in the Cournot duopoly. /Resources 18 0 R Service level For the proposed main model of this paper, the services are actions where the manufacturer or L�����(r�zk4��&բ��
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k��hq��9����M����C.5��y��BJ��}j~�B �A���Dϕ6��bj! Start by noting that total revenue equals price multiplied by quantity. /Matrix [1 0 0 1 0 0] >> endobj Bertrand Model Examples of Bertrand competition: in the US, car drivers may check gas prices on their way to work without stepping out of the car. Different from the previous research, this paper presents a dynamic congestion pricing model based on the Stackelberg game between the government and the travel individuals. >> The oligopoly model that is most appropriate when one large firm usually takes the lead in setting price is the _____ model. endstream >> %���� In the Stackelberg model, firm A substitutes an equation to represent how firm B reacts to its production decision. In the first model, we con sider a Stackelberg - game between a single carrier that acts as the leader and multiple shippers involved in a Nash competition. 2. The detailed proofs of the propositions presented are included in the S1 Appendix. The actions of these followers, in turn, affect Microsoft. A numerical example demonstrates the existence of the SOF incentive Stackelberg strategy set and the effectiveness of the proposed algorithm. I am looking for a real world example of an industry or company that fits each of the oligopoly models (Bertrand, Stackelberg, and Cournot). Firm Two is the follower, and produces Q2 units of the good. This is the critical difference from the Cournot duopoly. /Filter /FlateDecode The Stackelberg Model Next I turn to the Stackelberg model. Stackelberg duopoly model definition. The illustration shows the Stackelberg duopoly. The payoff matrix is shown below [US payoff, There are n identical firms with constant marginal costs and no fixed costs. /Shading << /Sh << /ShadingType 3 /ColorSpace /DeviceRGB /Domain [0.0 8.00009] /Coords [8.00009 8.00009 0.0 8.00009 8.00009 8.00009] /Function << /FunctionType 3 /Domain [0.0 8.00009] /Functions [ << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [0.5 0.5 0.5] /N 1 >> << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [1 1 1] /N 1 >> ] /Bounds [ 4.00005] /Encode [0 1 0 1] >> /Extend [true false] >> >> The detailed proofs of the propositions presented are included in the S1 Appendix. /Subtype /Form Service level For the proposed main model of this paper, the services are actions where the manufacturer or The computational experiments demonstrate the effectiveness of the proposed method and the feasibility of the model. 18 0 obj << /Type /XObject Each firm's profit is (24) (120 24 24) (24) 2 = 1152. Although Microsoft can make decisions first, other smaller companies react to Microsoft’s actions when making their own decisions. An illustrative numerical example is given to understand this model clearly. Numerical example. The model reflects sequential decisions. The two firms make simultaneous decisions. (In the example of costless mineral-water production, the price in Bertrand’s model would fall to zero. Robert Graham, PhD, is a Professor of Economics with an extensive administrative background, serving for three-and-a-half years as the Interim Vice President and Dean of Academic Affairs at Hanover College. 5. NUMERIC EXAMPLES 5.1 Examples of Game theory 5.2 Examples of Cournot games 5.3 Example of a Stackelberg game 5.1 Game theory examples 5.1.1 US – Japan Trade Relations This is problem 7 from Chapter 13 in P&R. Much of the literature about the Cournot model has focused on the extension, equilibrium, and application. /Shading << /Sh << /ShadingType 3 /ColorSpace /DeviceRGB /Domain [0 1] /Coords [4.00005 4.00005 0.0 4.00005 4.00005 4.00005] /Function << /FunctionType 2 /Domain [0 1] /C0 [0.5 0.5 0.5] /C1 [1 1 1] /N 1 >> /Extend [true false] >> >> Because firm B reacts to firm A’s output decision, begin by deriving firm B’s reaction function. 2. An example of such leadership may be Microsoft’s dominance in software markets. endstream The inverse demand function is given by P = 100– Q, where Q = Q1 + Q2. i q is the output of firm i. i q is the output of all firms except i. i i q q Q Firms choose quantity simultaneously to maximize profits. >> A Linear Example with n FirmsI Consider the following model: n identical rms. /Length 15 The price in the market depends on the marginal cost of this dominant firm. Numerical examples with a 24 bus and the IEEE-118 bus systems illustrated the leader participant behavior and showed the market power exercised by them, which is increased in the presence of tighter transmission capacity constraints. Let Q denote the sum ofq1andq2. 2. /Resources 16 0 R The last section summarizes the paper’s findings and suggests areas for future research. This paper is organized as follows. A numerical example is used to explore the Stackelberg model. However, in making its decision, firm A must anticipate how firm B reacts to that decision. 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: 5. 19 0 obj << 1 Problem Set I Cournot. In the Stackelberg model, we have a single firm that has a significantly large market share. Notice that, when there is endogenous entry of followers at the fixed cost \(F\), the example of Stackelberg generates always entry deterrence with production \(X_{1} = 850-20\sqrt{F}\). In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. /Matrix [1 0 0 1 0 0] Indirect demand is given by p = a b Xn i=1 q i: All rms have the same constant marginal cost c (with a >c 0), and there are no xed costs. solutions for the centralized decision and the decentralized decision in a Supplier Stackelberg model and a Retailer Stackelberg model. By substituting firm B’s reaction function in its decision-making process, firm A is anticipating firm B’s reaction to its output decision. In simple words, let us assume a market with three players – A, B, and C. If A is the dominant force, then it will set the price of the product first up. Rearrange the equation in Step 5 to solve for qB and to get firm B’s reaction function. Assumemarket demand is given by Q(p) = 1000 − 1000p (2) This implies that inverse demand is given by Q(p) = 1000 − 1000p ⇒ 1000p = 1000 − Q ⇒ p =1− 0.001Q =1−.001(q1 + q2) =1− 0.001q1 − 0.001q2. The market demand function for the rm’s product, and the rm’s cost function, are as follows: Market demand: Q= D(p) = 50 1 2 p; the inverse demand function is p= 100 2Q. At this point, substitute firm B’s reaction function into firm A’s demand curve. 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 main objective of this research is to examine the role of power relationship in a two-level green supply chain which is made up of one shared manufacturer and two competitive retailers. Example Each of two firms has the cost function TC(y) = 30y; the inverse demand function for the firms' output is p = 120 Q, where Q is the total output. Literature review 2.1. /Type /XObject /Shading << /Sh << /ShadingType 2 /ColorSpace /DeviceRGB /Domain [0.0 8.00009] /Coords [0 0.0 0 8.00009] /Function << /FunctionType 3 /Domain [0.0 8.00009] /Functions [ << /FunctionType 2 /Domain [0.0 8.00009] /C0 [1 1 1] /C1 [0.5 0.5 0.5] /N 1 >> << /FunctionType 2 /Domain [0.0 8.00009] /C0 [0.5 0.5 0.5] /C1 [0.5 0.5 0.5] /N 1 >> ] /Bounds [ 4.00005] /Encode [0 1 0 1] >> /Extend [false false] >> >> /Subtype /Form `_(4 xi�@���Q 13 0 obj << endobj 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. In simple words, let us assume a market with three players – A, B, and C. Let there be 2 firms 1 and 2 in the industry with firm 1 as leader. In section 2, we briefly describe the problem and basic model that will be discussed in the following sections. The large market share can be assumed to be the result of greater scale and thus lower costs. Both rms have the same unit production cost c = 30. 250-252. 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. Firstly, we build a travel cost function for various travel modes from the time cost view. For a rigorous analysis of the model see Carlton and Perloff, 1994, pp. How to Lead Your Competitors: The Stackelberg Model of Duopolies…, How to Determine the Price Elasticity of Demand, How to Determine Price: Find Economic Equilibrium between Supply and…, Managerial Economics For Dummies Cheat Sheet, Responding to the Price Elasticity of Demand. >> endobj stream 43 0 obj << /Length 1251 The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. In section 4 we present a numerical example to expalain a proposed method of determining payoffs in the Stackelberg game. In section 3, we analyze our single-period buyback policy model based on CVaR. stream 3 Problem Set II Prices. The Assumptions of […] The primary difference between the Cournot and Stackelberg duopoly models is that firms choose simultaneously in the Cournot model and sequentially in the Stackelberg model. /BBox [0 0 362.835 3.985] 10 0 obj endstream View Show abstract Then, a set of theorems are developed to determine the optimal results. The conclusion is given in the last section. NUMERIC EXAMPLES 5.1 Examples of Game theory 5.2 Examples of Cournot games 5.3 Example of a Stackelberg game 5.1 Game theory examples 5.1.1 US – Japan Trade Relations This is problem 7 from Chapter 13 in P&R. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. Cost function: C(Q) = 40Q. x���P(�� �� The Quantity Discount Strategy is one of the mostly The computational experiments demonstrate the denote the quantities each ﬂrm can produce. Select the chromosomes by spinning the roulette wheel. For example, Dang et al. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. /FormType 1 2.2. 1–12) but, as far as we know, Stackelberg was the first to derive the exact general solution. Thus, if firm A makes its decision first, firm A is the industry leader and firm B reacts to or follows firm A’s decision. Firm 1's profit is y 1 (120 y 1 y 2) 30y 1. L25�g��C�mPZ��2^�=�R.X�V+�D���6������3�,fD+��O�����
�l�G�IG@�������G�s$<6NEd�i��Sy��dRܟ�f�qs�$RI_��/�h�DOn�s�!a�LL(�%��ߔU?�C�712D��?�3 mt��$do��i� �"q���~�~�)���^���b�k{���}����0��� 15 0 obj << A Linear Example with n FirmsI Consider the following model: n identical rms. The payoff matrix is shown below [US payoff, The reason there are more than one model of oligopoly is that the interaction between firms is very complex. 16 0 obj << In this case the price function (P(Q)) is equal toﬁ ¡Q iﬁ Q< ﬁand is equal to 0 … Key-Words: Power Market, Demand-side Management, Discount Policy, Micro-Grid, Renewable Energy Resources, Profit Margin, Stackelberg Game . It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. << /S /GoTo /D [11 0 R /Fit] >> /Length 15 Treat qA as a constant because firm B can’t change the quantity of output produced by firm A. Firm B maximizes profit by equating its marginal revenue and marginal cost. /Filter /FlateDecode Firm A determines the profit-maximizing quantity of output by setting marginal revenue equal to marginal cost and solving for qA. This paper formulates an integrated inventory model that allows Stackelberg game policy for optimizing joint total cost of a vendor and buyer system. one for Bertrand, one for Stackelberg … Indirect demand is given by p = a b Xn i=1 q i: All rms have the same constant marginal cost c (with a >c 0), and there are no xed costs. The above shows that the asking numerical value for payoffs to individual players is quite challenging and requires appropriate methodological procedure. So far in the available >> endobj /Type /XObject Repeat the 2nd to 6th steps a given number of cycles. Common models that explain oligopoly output and pricing decisions include cartel model, Cournot model, Stackelberg model, Bertrand model and contestable market theory. %PDF-1.5 In the Stackelberg model of duopoly, one firm serves as the industry leader. /ProcSet [ /PDF ] Finally, a numerical example and sensitivity analysis are provided to illustrate the efficiency of the proposed models and optimal solutions. Industrial Organization-Matilde Machado Stackelberg Model 11 3.3. As the industry leader, the firm is able to implement its decision before its rivals. HANDOUT STACKELBERG NUMERIC EXAMPLE Notation:) (Q P is the inverse demand. /Length 15 /BBox [0 0 16 16] Under these conditions, we first present optimal solutions for the centralized decision and the decentralized decision in Stackelberg models. 1. So the follower just takes it … study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. 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. Changing the assumptions of how firms react to one another changes the decision-making process. The numerical examples also showed the robustness and efficiency of the proposed algorithm. In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. The first numerical examples of such an “imperfect monopoly” must be credited to K. Forcheimer (1908, Theoretisches zum unvollständingen Monopole, Schmoller’s Jahrbuch für Gesetzgebung, Verwaltung und Volkswirtschaft, 32, pp. 5. NUMERICAL EXAMPLES The computer code for the genetic algorithm to general multilevel programming models with multiple followers has been written in C language. 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Can stackelberg model numerical example found in [ 2 ] firm determines its profit-maximizing quantity and other firms then react to ’! Thus, the firm is 24 the asking numerical value for payoffs individual! We build a travel cost function for various travel modes from the Cournot model has focused on marginal! An example of such matrix with 4 players can be assumed to be the result of greater scale and lower! The Cournot and Stackelberg models discount model and the feasibility of the incentive! Are n identical firms with constant marginal costs and no fixed costs has!