Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium. (You may assume that firm X can only choose quantities that are multiples of 200. This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. ) ### Cournot Nash Equilibrium Graph Analysis#### Data Table| Y | X ||-----|-----|| 0 | 600 || 200 | 500 || 400 | 400 || 600 | 300 |#### Graph ExplanationThe graph demonstrates the Cournot Nash Equilibrium between two firms, Firm X and Firm Y. The x-axis (labeled as Qx) denotes the quantity produced by Firm X, ranging from 0 to 1200 in increments of 100. The y-axis (labeled as Qy) indicates the quantity produced by Firm Y, ranging from 0 to 1200, also in increments of 100.- The solid line labeled "Firm X" starts from (Qx=1200, Qy=0) and declines to (Qx=0, Qy=600).- The solid line labeled "Firm Y" starts from (Qx=0, Qy=0) and inclines to (Qx=1200, Qy=600).These lines represent the reaction functions for Firm X and Firm Y, respectively. The point where the two lines intersect, labeled as E (400, 400), signifies the Cournot Nash Equilibrium, where both firms produce 400 units.#### ExplanationAt the intersection of the two reaction functions (denoted by point E), the quantities for both firms are equal at 400 gallons each. This point of intersection represents the Cournot Nash Equilibrium. To arrive at this intersection point, the two reaction functions were solved, showing that $ Qx = Qy = 400 $. This equilibrium point indicates that both firms' production behaviors are optimal given the output of the other firm.

To determine the Nash equilibria which is subgame perfect, we will use the extensive form…

Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium.

Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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Two firms, X and Y, are involved in a price war. The demand equations for each firm are the following: Qx = 52 - 2Px + Py Qy = 52 - 2Py + Px Further, assume the cost of each unit of out is constant at $4. What is the Nash equilibrium of this game? (Use the best response functions in a graph to answer) There is no Nash equilibrium O $24 $20 $22
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am. 158.
We can see from the payoff matrix that there are no pure strategy Nash equilibrium in this game because at least one firm would always have an incentive to change its behavior. From Nash's theorem, we know there must be at least one Nash equilibrium so there must be a mixed strategy Nash equilibrium for this game. Find the mixed strategy Nash equilibrium by first deleting all dominated strategies in the game What's the expected payoff to Firm 1 in the equilibrium?
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Player 2 X Y Player X (3,3) (0,4) 1 Y (4,0) (2,2) Figure 9.18 Find all the subgame perfect Nash equilibria of this supergame. Also, briefly explain why each one is subgame perfect.
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Exercise 6.7. Suppose two identical companies produce wood stoves and they are the only ones on the market. Its costs are given by: C1 (q1 )=200q1 and C2 (q2) = 200q2. And the inverse market demand curve is: P=2000-2Q, where Q =q1 + q2 Get the Cournot-Nash equilibrium. Calculate the profits of each company. Show graphically. Suppose that the two companies form a cartel to maximize joint profits. How many stoves will you produce? Calculate the profits of each company. Represent graphically. Managers now note that explicit agreements to collude are illegal. Each company must decide on its own whether to produce the amount of Cournot or that of the cartel.