Econ 171
Fall 2008
Exam 2
November 13
You have 75 minutes to take this exam. Please answer all 4 questions. Each question is worth
25 points and point subtotals are in brackets. To obtain credit, you must provide arguments
or work to support your answer.
1. Consider the game shown in Figure 1, where if both players choose
R
, they then play
a
simultaneous
BoS game, as given in Figure 2.
(a) [2] Draw the full extensive form representation of the game, i.e. draw the tree
with the BoS included in the extensive form.
(b) [2] List the strategies for each player.
(c) [1] How many subgames does this game have?
(d) [5] Find all the Nash equilibria of this game
(e) [10] Which of these are subgame perfect?
(f) [5] Now suppose that the if both players choose
R
, the game they play is
sequential
BoS with Player 2 going frst
.
1. How many subgames are there?
2. Solve by backwards induction and report the resulting strategy pro±le.
R
L
2
,
2
1
R
BoS
L
3
,
1
2
Figure 1: If both players choose
R
,theyp
layBOS
OB
O
2
,
1
0
,
0
B
0
,
0
1
,
2
Figure 2: BoS
2. Consider a fourperiod bargaining game in which Player 1 would make the o²er in
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 Fall '08
 Charness,G
 Game Theory, player, SubgamePerfect Nash Equilibrium

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