a. Are there any values for r' and y' such that there are two Nash equilibria in pure strategies? If yes, for what values of x' and y'? If no, carefully explain why not. b. Are there any values for x' and y' such that there is a dominant strategy equilibrium in which both firms play High? If yes, for what values of x' and y? If no, carefully explain why not. c. Are there any values for r' and y' such that Firm A has a dominant strategy but Firm B does not? If yes, for what values of x' and y'? If no, carefully explain why not.

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter10: Monopolistic Competition And Oligopoly
Section: Chapter Questions
Problem 13PAE
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The question is intermediate microeconomics

Question 1 (Game Theory)
Two firms, Firm A and Firm B, are the only producers in a market for a particular good.
Each firm can choose to produce either Low or High output. If both firms choose Low output,
the payoffs are (300, 250) (throughout, a pair of payoffs (x, y) represents x profits for Firm
A, and y profits for Firm B). If they choose different outputs the payoffs are (200, 75) when
Firm A chooses High output and (200, 100) when Firm A chooses Low output. If both firms
choose High output, the payoffs are (x', y').
a. Are there any values for x' and y' such that there are two Nash equilibria in pure
strategies? If yes, for what values of x' and y'? If no, carefully explain why not.
b. Are there any values for r' and y' such that there is a dominant strategy equilibrium
in which both firms play High? If yes, for what values of x' and y'? If no, carefully
explain why not.
c. Are there any values for r' and y' such that Firm A has a dominant strategy but Firm
B does not? If yes, for what values of x' and y'? If no, carefully explain why not.
Transcribed Image Text:Question 1 (Game Theory) Two firms, Firm A and Firm B, are the only producers in a market for a particular good. Each firm can choose to produce either Low or High output. If both firms choose Low output, the payoffs are (300, 250) (throughout, a pair of payoffs (x, y) represents x profits for Firm A, and y profits for Firm B). If they choose different outputs the payoffs are (200, 75) when Firm A chooses High output and (200, 100) when Firm A chooses Low output. If both firms choose High output, the payoffs are (x', y'). a. Are there any values for x' and y' such that there are two Nash equilibria in pure strategies? If yes, for what values of x' and y'? If no, carefully explain why not. b. Are there any values for r' and y' such that there is a dominant strategy equilibrium in which both firms play High? If yes, for what values of x' and y'? If no, carefully explain why not. c. Are there any values for r' and y' such that Firm A has a dominant strategy but Firm B does not? If yes, for what values of x' and y'? If no, carefully explain why not.
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