stackelberg model numerical example

>> endobj In the Stackelberg model of duopoly, one firm serves as the industry leader. Report the best chromosome as the optimal solution. Firm A’s marginal revenue is the derivative of total revenue taken with respect to qA. The outer approximation method is applied to solve the mixed integer nonlinear programming problem. 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. The equilibrium price will be the competitive price. For this purpose was used a model of Stackelberg duopoly. 43 0 obj << >> What is the Stackelberg Model? 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. HANDOUT STACKELBERG NUMERIC EXAMPLE Notation:) (Q P is the inverse demand. 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. The detailed proofs of the propositions presented are included in the S1 Appendix. Finally, we provide a numerical example and sensitivity analysis to illustrate the efficiency of the proposed models and optimal solutions. 20 0 obj << In the Stackelberg model, firm A substitutes an equation to represent how firm B reacts to its production decision. 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. >> 1 Introduction . 19 0 obj << This is the major contribution of the paper. /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] >> >> /ProcSet [ /PDF ] `_(4 xi�@��Q ADVERTISEMENTS: The Cournot Model and the Cournot Solution: The first systematic oligopoly model was published by the French economist Antoine Augustin Cournot (1801-77) in 1838. stream endstream /FormType 1 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. /Matrix [1 0 0 1 0 0] 2. The payoff matrix is shown below [US payoff, NONCOOPERATIVE OLIGOPOLY MODELS 3 3.2.2. >> endobj It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. The conclusion is given in the last section. Let Q denote the sum ofq1andq2. The last section summarizes the paper’s findings and suggests areas for future research. For price, substitute the equation from Step 2. At this juncture I will point Out the informational asymmetries in the Cournot and Stackelberg model. The two firms make simultaneous decisions. the numerical examples and analysis are presented. The reason there are more than one model of oligopoly is that the interaction between firms is very complex. L��(r�zk4��&բ�� ,XJacf�gr�X(�Y��4֫xw�7��&Y$a7��r��?Z�Wy�d��K H��`�ҹ�EF}ʤVH��p`^U�VJ�7E�nB��Ve��l�ݞ%��C{��a��h��7�Kā��ݏ`��&R�: k��hq��9��M��C.5��y��BJ��}j~�B �A��Dϕ6��bj! Finally, a numerical example and sensitivity analysis are provided to illustrate the efficiency of the proposed models and optimal solutions. 17 0 obj << x��P(�� The Cournot and Stackelberg models have been widely studied in the literature. Our model extends Sherali’s deterministic multiple-leader model (Sherali 1984) because it considers the case where (EXCESS ENTRY) (Vives 4.12) Consider a Cournot market with linear demand P = a bQ; a > 0; b > 0 and zero marginal costs for all the –rms. This is the major contribution of the paper. View Show abstract The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. Much of the literature about the Cournot model has focused on the extension, equilibrium, and application. /Matrix [1 0 0 1 0 0] << /S /GoTo /D [11 0 R /Fit] >> x��P(�� Most textbooks present an adequate explanation of the model. /ProcSet [ /PDF ] The model is ‘closed’-does not allow entry. I.E. This model assumes that there are two firms in the industry, but they are asymmetrical: there is a “leader” and a “follower.” Stackelberg used this model of oligopoly to determine if there was an advantage to going first, or a “first-mover advantage.” A numerical example is used to explore the Stackelberg model. Because firm B reacts to firm A’s output decision, begin by deriving firm B’s reaction function. stream >> endobj Common models that explain oligopoly output and pricing decisions include cartel model, Cournot model, Stackelberg model, Bertrand model and contestable market theory. /Resources 13 0 R Thus. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. Firm Two is the follower, and produces Q2 units of the good. In section 4, we apply a numerical example to simulate the model … /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] >> >> Assume that firm A has a constant marginal cost of $20 and firm B has a constant marginal cost of $34. (r+1) personal Stackelberg game [4]. 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 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. It was formulated by Heinrich Von Stackelberg in 1934. 5. /BBox [0 0 5669.291 8] >> Numerical example of such matrix with 4 players can be found in [2]. 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. There are n identical firms with constant marginal costs and no fixed costs. Rearrange the equation in Step 5 to solve for qB and to get firm B’s reaction function. 2. Stackelberg model. 2. The illustration shows the Stackelberg duopoly. In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. If there are two gas stations in the same route, since gas is a homogenous good, the driver will stop at the cheapest one. stream The Quantity Discount Strategy is one of the mostly HANDOUT STACKELBERG NUMERIC EXAMPLE Notation:) (Q P is the inverse demand. Assume two firms, where Firm One is the leader and produces Q1 units of a homogeneous good. A Linear Example with n FirmsI Consider the following model: n identical rms. 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. 2. Note that firm B has exactly the same reaction function as existed in the Cournot duopoly. For example, Dang et al. The leader’s output has already been produced. >> 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. The detailed proofs of the propositions presented are included in the S1 Appendix. A numerical example demonstrates the existence of the SOF incentive Stackelberg strategy set and the effectiveness of the proposed algorithm. The outer approximation method is applied to solve the mixed integer nonlinear programming problem. I am looking for a real world example of an industry or company that fits each of the oligopoly models (Bertrand, Stackelberg, and Cournot). The payoff matrix is shown below [US payoff, As the industry leader, the firm is able to implement its decision before its rivals. 1. endobj Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity s n ≥0 • Cost of producing s n: c n s n /FormType 1 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. study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. The computational experiments demonstrate the The price in the market depends on the marginal cost of this dominant firm. Although Microsoft can make decisions first, other smaller companies react to Microsoft’s actions when making their own decisions. In this paper, we consider a stochastic multiple-leader Stackelberg-Nash-Cournot (SMS) equilibrium model. 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. Substitute qA and qB for QD in the market demand curve to yield. Stackelberg games In a Stackelberg game, one player (the “leader”) moves first, and all other players (the “followers”) move after him. Firm A determines the profit-maximizing quantity of output by setting marginal revenue equal to marginal cost and solving for qA. Contract decision models including quantity discount model and the Stackelberg game theoretic model are studied. In the Stackelberg model, we have a single firm that has a significantly large market share. Assume that demand is given by D(p) = a bP and –rms are symmetric with cost function given by C(q) = c 2 q 2.Find the Bertrand equilibria as a function 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. 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. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] 7. 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. Treat qA as a constant because firm B can’t change the quantity of output produced by firm A. NUMERICAL EXAMPLES The computer code for the genetic algorithm to general multilevel programming models with multiple followers has been written in C language. Numerical example. The simultaneous decision-making associated with the Cournot model leads to different outcomes from the outcomes associated with sequential decisions of the Stackelberg model. /BBox [0 0 16 16] For a review of various extensions and applications of … This paper formulates an integrated inventory model that allows Stackelberg game policy for optimizing joint total cost of a vendor and buyer system. 13 0 obj << 5. 16 0 obj << In simple words, let us assume a market with three players – A, B, and C. x��P(�� 5. In this case the price function (P(Q)) is equal toﬁ ¡Q iﬁ Q< ﬁand is equal to 0 … Repeat the 2nd to 6th steps a given number of cycles. Production decision, discount policy, Micro-Grid, Renewable Energy Resources, profit Margin, Stackelberg game B profit. 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