Exercise 2: Cournot Oligopoly The inverse market demand is 0 if Q≥ 220 P(Q) 220 Q if Q< 220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10g, for i = {1, 2}. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits in equilibrium. 2. Suppose firm 1's cost function is still c₁(91) 10g Firm 2 has an avoidable fixed cost, resulting in the cost function 0 c2(92) if q2=0 10g2+3,600 if q2 > 0. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. 3. Suppose there are nЄ N, n > 2 identical firms with cost functions c, (q;) 10q for iЄ {1, 2,...,n}. Find the payoff functions and best responses for all firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits (as functions of n) in equilibrium. Discuss how the market price and profits react to an increase in the number of firms n. What happens in the limit as n goes to infinity?

Exercise 2: Cournot Oligopoly The inverse market demand is 0 if Q≥ 220 P(Q) 220 Q if Q< 220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10g, for i = {1, 2}. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits in equilibrium. 2. Suppose firm 1's cost function is still c₁(91) 10g Firm 2 has an avoidable fixed cost, resulting in the cost function 0 c2(92) if q2=0 10g2+3,600 if q2 > 0. Find the payoff functions and best responses for both firms. Identify all Nash equilibria of this game. 3. Suppose there are nЄ N, n > 2 identical firms with cost functions c, (q;) 10q for iЄ {1, 2,...,n}. Find the payoff functions and best responses for all firms. Identify all Nash equilibria of this game. Compute the market price and the firms' profits (as functions of n) in equilibrium. Discuss how the market price and profits react to an increase in the number of firms n. What happens in the limit as n goes to infinity?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

See similar textbooks

Similar questions

Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.
Let G be the following static game. Rose Colin A A (3,4) B (4,2) B (1,5) (0, 1) (a) Determine the pure Nash equilibria of G. (b) Rose A, B, Colin A, B is a mixed Nash equilibrium of H. (You do not have to verify this.) Determine the expected payoffs of both players given that they choose their strategies according to this Nash equilibrium. (c) Draw the payoff polygon of H. Indicate on your diagram the points corresponding to the Nash equilibria of H, and the points corresponding to Pareto optimal solu- tions of H.
QS. Consider the following stage game B. C A (4, 4) (1, 5) (0, 3) B (7, 1) (3, 4) (0, 1) C (3, 0) (2, 0) (1, 1) (a). Find all Nash equilibria of the stage game (b). Suppose that the stage game is played two times and with agents discount factor given by 0<6 <1. Is there a subgame perfeet equilibrium equilibrium strategy profile in which (A, A) is played in the first round? If not explain whv. (Hint: Think of o 1)
• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)
Please correct answer and don't use hand rating
find the Nash equilibria in mixed strategies...
Find the Nash Equilibria for each of the following 2x2 games (The left payoff value is associated with the strategies (1 or 2) while the right payoff value is associated with the strategies (A or B)): (a) (b) (c) (d) B 1 3,3 2 4,4 5,5 1 2 1 2 1 2 A 2,2 24 A B 2,5 0,3 4,0 -5,2 A 1,0 0,6 B 4,1 5,5 A B -1,-3 -3,2 -4,1 0,0
A large group of players each guesses a number between 0 and 300. The winner is the person whose number is closest to three-fifth of the average guess. What is the Nash equilibrium? Will it be observed? What do you expect for the outcome of this game with next year's 203 class? (Considering that they have similar sophistication to your class but they have not covered game theory yet.)
Please answer fast
Please no written by hand solution Consider a Hotelling Game with 8 homogeneous firms. Customers are uniformly distributed on the interval [0, 1] and each customer goes to the firm closest to his own location. If firms are located in the same spot, they share the customers evenly. Firms choose their location to maximize customers. How many Nash equilibrium(/ia) does this game have?
What are the sub games in the following game? Find all subgame perfect Nash equilibria (SPNE)
Find ALL pure-atrategy Subgame Nash Equilibria (you may ignore mixed strategies). Be sure to pay attention to which player is which! N Y 2,2 R R 4, 4 8,2 2,8 0,0 2)