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Exercise 2: Cournot Oligopoly The inverse market demand is P(Q)= { 0 if Q≥ 220 220 Q if Q<220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10q, 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) = 10q1. Firm 2 has an avoidable fixed cost, resulting in the cost function C2 (92) 0 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 i = {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 P(Q)= { 0 if Q≥ 220 220 Q if Q<220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10q, 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) = 10q1. Firm 2 has an avoidable fixed cost, resulting in the cost function C2 (92) 0 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 i = {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
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Exercise 2: Cournot Oligopoly The inverse market demand is P(Q)= { 0 if Q≥ 220 220 Q if Q<220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10q, 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) = 10q1. Firm 2 has an avoidable fixed cost, resulting in the cost function C2 (92) 0 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 i = {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?
Transcribed Image Text:Exercise 2: Cournot Oligopoly The inverse market demand is P(Q)= { 0 if Q≥ 220 220 Q if Q<220 where Q = Ziel i 1. Suppose there are two identical firms with cost functions c(q) = 10q, 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) = 10q1. Firm 2 has an avoidable fixed cost, resulting in the cost function C2 (92) 0 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 i = {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?
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