Professor Rod Garratt
Fall 2004
Final Exam, Econ 210B
You have 2 hours. Explain everything that needs explaining. Good Luck!
1.
Consider the following twoplayer game,
Γ
. Each player can either work hard (h) or
shirk (s). If both work hard they each get a payoff of 2. If both shirk they each get a
payoff of 0. If one shirks and the other works hard, the person who works hard gets a
payoff of –1 and the person who shirks gets a payoff of 0. The game
Γ
is preceded by
another simultaneous game in which the two players announce whether they wish to
“Play” or “Not Play” the game
Γ
. If they both announce “Play” then they play the
game
Γ
. Otherwise, each gets a payoff of 1, i.e., strategy profiles (Play, Not Play),
(Not Play, Play) and (Not Play, Not Play) give each player a payoff of 1.
(a)
Compute all the Nash equilibria of the subgame
Γ
.
(4 points)
(b)
Is there a subgameperfect equilibrium in which both players choose shirk with
positive probability in the subgame
Γ
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 Fall '09
 GARRATT
 Game Theory, Mixedstrategy Nash equilibrium, evil dictator

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