7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 4 and Aaliyah will receive a payoff of 4. Aaliyah Up Down Up 6,5 4,4 Russell Down 5,3 7,2 In this game, the only dominant strategy is for Russell to choose Down The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses Down and Aaliyah chooses Up .
7. Solving for dominant strategies and the Nash equilibrium Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and Aaliyah chooses Down, Russell will receive a payoff of 4 and Aaliyah will receive a payoff of 4. Aaliyah Up Down Up 6,5 4,4 Russell Down 5,3 7,2 In this game, the only dominant strategy is for Russell to choose Down The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses Down and Aaliyah chooses Up .
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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Transcribed Image Text:7. Solving for dominant strategies and the Nash equilibrium
Suppose Russell and Aaliyah are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows
shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Russell chooses Up and
Aaliyah chooses Down, Russell will receive a payoff of 4 and Aaliyah will receive a payoff of 4.
Aaliyah
Up
Down
Up
6,5
4,4
Russell
Down
5,3
7,2
In this game, the only dominant strategy is for Russell
to choose Down
The outcome reflecting the unique Nash equilibrium in this game is as follows: Russell chooses Down
and Aaliyah chooses Up .
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