Question from Past Microeconomics Qualifying ExamEdit
Fall 2005 - Section I, Question six, George Mason University
T, F, U. State first whether the following statements are true, false or uncertain. Then briefly explain your reasoning in four or five sentences. You may use a graph if it helps clarify your answer.
The Prisoners' Dilemma has one strictly dominant outcome and one Nash equilibrium. The Hawk-Dove Game has no Strictly Dominant outcomes and two Nash equilibria.
AnswerEdit
True. The Prisoners' Dilemma does have one strictly dominant outcome and one Nash equilibrium. Under the following scenario, it is a dominant strategy for both players to confess.
PRISONER'S DILEMMA | ||
---|---|---|
Confess | Don't Confess | |
Confess | (1,1) | |
Don't Confess | | |
The Hawk-Dove game has no stricly dominant outcomes and two Nash equilibria. Of course, a mixed-strategy Nash equilibrium can be found where both players alternate between fight and don't fight. In this case each player would choose to fight 10% of the time. (NOTE: This assumes cardinal utility.)
HAWK AND DOVE | ||
---|---|---|
Fight | Don't Fight | |
Fight | | (10,-10) |
Don't Fight | (-10,10) | |
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