Two firms must simultaneously decide whether to enter a market. The payoffs resulting from their decisions are illustrated in the figure to the right. Determine the mixed-strategy Nash equilibrium for this game. The mixed-strategy Nash equilibrium is for Firm 1 to not enter with probability 0₁ = probability 0₂ = (Enter your responses rounded to two decimal places.) and for Firm 2 to not enter with Don't enter Firm 2 Enter Don't enter 0 0 Firm 1 0 Enter 0 -4 2 -2

Two firms must simultaneously decide whether to enter a market. The payoffs resulting from their decisions are illustrated in the figure to the right. Determine the mixed-strategy Nash equilibrium for this game. The mixed-strategy Nash equilibrium is for Firm 1 to not enter with probability 0₁ = probability 0₂ = (Enter your responses rounded to two decimal places.) and for Firm 2 to not enter with Don't enter Firm 2 Enter Don't enter 0 0 Firm 1 0 Enter 0 -4 2 -2

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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Intel and AMD are the two dominant producers of microchip processors. The following matrix gives the payoffs (in millions of dollars) of the two firms for different combinations of their pricing strategies. The first number is Intel's payoff and the second AMD's. AMD Intel Low Price High Price Low Price 35, 30 30, 60 High Price 70,25 65,55 O If this game is played sequentially, the Nash equilibrium will not change irrespective of who moves first. If this one-shot game is repeated for 10 times, the Nash equilibrium is for both firms to choose High Price. O In this game, Pareto criterion leads both firms to choose High Price. This game is an example of coordination game.
Two firms must simultaneously decide whether to enter a market. The payoffs resulting from their decisions are illustrated in the figure to the right. Determine the mixed-strategy Nash equilibrium for this game. The mixed-strategy Nash equilibrium is for Firm 1 to not enter with probability not enter with probability 0₂ - (Enter your responses rounded to two decimal places) and for Firm 2 to Don't enter Firm 2 Enter Don't enter 10 Firm 1 0 Enter 5
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2: Provide a definition for a Nash equilibrium and then find all pure-strategy Nash equilibria of the following game: Left Center Right Up Middle 1,3 2,7 6,3 2,9 4,4 7,10 Down 3,8 2,5 3,4
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Consider a two-player game in which the players take turns, with player 1 moving first. When it is a player's turn, she must announce a number between 1 and 3. The announced number is added to the previously announced numbers. The player who announces the number such that the sum of all announced numbers is 6 wins (receives 1) and the other loses (receives 0). Please indicate whether or not each of the following sequences of announcements is a Nash equilibrium of the game. Hint: Think about how one verifies whether or not a pair of strategies is a Nash equilibrium. P1 says 3, then P2 says 2, then P1 says 1 P1 says 1, then P2 says 3, then P1 says 2 P1 says 2, then P2 says 3, then P1 says 1 P1 says 3, then P2 says 1, then P1 says 2
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O Cell A O Cell C O Cell E O Cell I None of the above
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