Topic 4: Duopoly: Cournot-Nash Equilibrium. a) Find the Stackelberg equilibrium outputs for firms A and B, the equilibrium market price and the equilibrium profit for each firm, on the assumption that firm A is the leader and firm B is the follower. Many works studied on complex dynamics of Cournot or Stackelberg games, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase. A calculate the stackelberg market equilibrium price. Stackelberg equilibrium JEL Classifications: C72; H26; H62, H63. GAME THEORY DEFINITIONS 1.1 Dominant strategy 1.2 Nash Equilibrium 1.3 Maximin … In the Stackelberg model, the firm that sets output first has an advantage. ): P Industrial Economics-Matilde Machado 3.2. 360 Accesses. π'2 = 800 - 150 - Q2/2 -2Q2 - 500. The situation is known as Stackelberg’s disequilibrium and the effect will either be a price war until one of the firms surrenders and agrees to act as follower, or a collusion is reached, with both firms abandoning their naive reaction functions and moving to a point closer to (or on) the Edge-worth contract curve with both of them attaining higher profits. plug in Q1 from previous calculation. Springer, Heidelberg, New York, 2011. b) Repeat for i. ii. Stackelberg equilibrium. Hardcover, £ 81.00 . 5. The wireless body sensors are placed to observe the patient's activities and monitor the medical records with high security level. Stackelberg Equilibrium (SE) (Leitmann 1978) defines equi-librium profile for two-player asymmetric games. Numeric Examples: applying these concepts to exercises. For gamma-distributed rates of claim arrivals, explicit equilibrium premiums are obtained, and shown to depend on the running reserve difference. A stationary feedback Stackelberg equilibrium with player 2 as the leader can be defined analogously, by interchanging the roles of the players. The Bertrand Model: what happens when two firms compete simultaneously on the price of a homogenous good. The app endices con tain most of the mathematical calculations. Federico Etro 1 Journal of Economics volume 109, pages 89 – 92 (2013)Cite this article. Cournot Model Graphically (cont. The set of Stackelberg equilibria (red) in a particular game is determined as the solution-of-optimization problem on the graph-of-best-response mapping (blue) of the player 2 (follower); its vertices are given at the bottom. COURNOT DUOPOLY: an example Let the inverse demand function and the cost function be given by P = 50 − 2Q and C = 10 + 2q respectively, where Q is total industry output and q is the firm’s output. Q2 would be . One player { the Leader { commits to a certain strategy and the other player { the Follower { de nes his/her strategy being aware of the Leader’s commitment. If the second firm decided to produce a larger quantity, this would reduce price and profit for both firms. 4. Explain why. Numerical experiments are carried out to verify the effectiveness of the proposed algorithms. 4. Stackelberg-Nash Equilibrium 85 Step Step Step Step Step Step Step 2. Again this equilibrium is subgame perfect and also dynamically consistent. Extraproximal Method Application for a Stackelberg–Nash Equilibrium Calculation in Static Hierarchical Games May 2009 IEEE transactions on systems, man, and cybernetics. School Urbana University; Course Title BSG 502; Type. Sorry for always asking for help but my teacher really isn't that good.... 0. reply. In Cournot model, when there are many competitions, the competitive equilibrium becomes chaotic. STACKELBERG PREDICTION GAME We model the prediction game as a Stackelberg compe-tition; we refer to the resulting model as the Stackelberg prediction game (SPG). 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.. Thus, the Stackelberg equilibrium can be calculated in polynomial time. Stackelberg Equilibrium (SE) Leitmann (1978) de nes equilibrium pro le for two-player asymmetric games. Incidentally, in many textbooks, Cournot competition is cited as the application of Nash equilibrium. Q2 = 100 at zero. Rep:? We now turn to the situation when there are a small number of firms in the industry and these firms have the option of colluding with or competing with each other. Typically, as the price goes up, demand goes down, but this varies with every market. The simulation of 25 milliseconds is taken to carry out single process. Cournot Model Graphically: Let’s assume the duopoly case (n=2) MC=c Residual demand of firm 1: Industrial Economics-Matilde Machado 3.2. But when multiple strategies are not different for followers, the concept cannot guarantee a unique solution. In a demand curve, the quantity demanded (Q) is a function of price (P), which is Q = f(P). Cournot Model 3 RD1(p,q2)=D(p)-q2. If K 1 > K 2 and I 2 is the leader choosing its premium first, conditions for Stackelberg equilibrium are established. The firm with the highest price will not receive any purchases. The calculation of the Stackelberg–Nash equilibrium as a fixed point problem in static hierarchical games September 2018 International Journal of Dynamics and Control 6(1):1-12 My Workings I've tried to solve the problem using the following method: raksmax Badges: 1. Calculate the quantity produced by firms in this economy, and compare it to Cournot outcome with 3 firms and to Stackelberg outcome with 2 firms. Game Theory with Stackelberg Security Equilibrium (GTSSE) is implemented in NS-2 simulator with the network range of 1000∗1000 m size. Stackelberg, Heinrich von: Market Structure and Equilibrium. 2 The cartel-v ersus-fringe mo del The supply side of some mark ets for exhaustible natural resources, suc h as the oil mark et, can b e c haracterized b y a large coheren t cartel and a big n um b er of small suppliers called the fringe. If prices are equal, purchases will be split. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. To begin with, we assume that there are only two firms---a situation called duopoly. Homework Help. Stackelberg equilibrium. This is a preview of subscription content, log in to check access. JEL Codes: C72; H23; Q52; H62. The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. Stackelberg equilibrium is a refinement of the Nash equilibrium concept in a Stackelberg game. Metrics details. • The Stackelberg equilibrium prices are: pS 1 =17 p S 2 =14.5. Introduction In this paper we deal with the dynamics of accumulation of a nation’s public debt which harms prosperity of the economic agents of a country or a nation. The Stackelberg Model: what happens when two firms compete sequentially on the quantity of output they produce of a homogeneous good. 2 1. Next, we explain how the dynamic programming approach can be used to calculate the equilibria we have just de fined. How would I go about calculating this? Green points are not equilibrium, but have the same value of the cost function of the leader on the interior vertex of the set of Stackelberg equilibria. 1. Update the chromosomes by crossover and mutation operations. A Calculate the Stackelberg market equilibrium price output solutions B How do. This preview shows page 25 - 28 out of 37 pages. Therefore, both of them would intend to remain on their respective reaction functions. There is no previous research to explore a further problem with the general equilibrium points of n-contenders in Cournot model. The concept is that consumers will purchase from the company with the lowest price. Equilibrium in the Cournot Model—Competitive, Monopoly and Duopoly Solutions: We have seen above that the reaction functions of the duopolists have been derived from the profit-maximising conditions, and by assumption, both the duopolists pursue the profit- maximising goal. Introduction In this paper we deal with the dynamics of accumulation of a nation’s public debt which harms prosperity of the economic agents of a country or a nation. Plugging this result in Q1 we get Q1 = 100. and then we get the price P = 800 - 100 - 100 = 600 . 5 Citations. Before calculating the Cournot equilibrium point, you must first know the demand curve for your market. Determine the NasA equilibrium for each chromosome (control vector of leader) by iterative methods or genetic algorithms. Uploaded By KidHackerIbex10348. 3.2. 4) Analyses and experiments for proposed algorithms: The convergences as well as computational complexities of the proposed 3 algorithms are analyzed, respectively. I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). Access options Buy single article. the case where the marginal cost of firm B is constant and equal to 7. A. 3. One player – the Leader – commits to a certain strategy and the other player – the Follower – defines his/her strategy be- ing aware of the Leader’s commitment. t equilibrium for the cartel-v ersus-fringe mo del. Furthermore, two versions of a heuristic algorithm based on a modified TA and a DE approaches were proposed to solve the model. The problem of the firm with residual demand RD is similar to the monopolist’s. The Cournot equilibrium is what happens if both firms are optimising their response so you solve them as simultaneous equations: ... since the two firms are competing in prices, then this is bertrand competition correct? To obtain the Stackelberg–Nash equilibrium solution, the problem was modeled as a bi-level optimization model. Then in the next Topic we will consider a larger number of firms---first four and then ten. XII, 134pp. Calculate the objective values of the leader for all chromosomes according to the NasA equilibrium reactions of … They say "we define a Stackelberg strategy as one which involves taking into account the contemporaneous reaction of one's rival in setting one's own strategy". In addition, the proposed algorithm has been evaluated using test-suite of SMD test problems. This flexibility, however, would hurt firm 1 since firm 2 would anticipate this reaction and the result could be no other but Cournot. The reason is that at the end of period 2, after firm 2 has decided on q2, firm 1 would like to change its decision and produce the best response to q1, R 1(q 2). To study how to calculate a Cournot equilibrium, see [1]. The Bertrand Equilibrium model describes consumer purchasing behavior based on prices of products. In the Random Way Point Model (RWM), each mobile … In this equilibrium, each player will choose the best response in each sub-game of the original game. Equilibrium (Cournot-Nash) 3.2. The Stackelberg leader gains an advantage because the second firm must accept the leader’s large output as given and produce a smaller output for itself. Under the assumption that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Stackelberg–Cournot game with heterogeneous expectations is considered in this paper. 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