Consider the following coordination game: Player 2 P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game. b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’s outcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarian preferences. c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as a negative outcome for the individual, ρ = σ = -1. Find the Nash equilibrium(s) with these envious preferences.
Consider the following coordination game: Player 2 P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game. b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’s outcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarian preferences. c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as a negative outcome for the individual, ρ = σ = -1. Find the Nash equilibrium(s) with these envious preferences.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Question
Consider the following coordination game:
Player 2
P1
| Comedy Show | Concert | |
| Comedy Show | 11,5 | 0,0 |
| Concert | 0,0 | 2,2 |
a. Find the Nash equilibrium(s) for this game.
b. Now assume Player 1 and Player 2 have distributional preferences.
Specifically, both people greatly care about the utility of the other person.
In fact, they place equal weight on their outcome and the other person’s
outcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarian
preferences.
c. Now consider the case where Player1 and Player2 do not like each other.
Specifically, any positive outcome for the other person is viewed as a
negative outcome for the individual, ρ = σ = -1. Find the Nash
equilibrium(s) with these envious preferences.
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