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S’11
Prof. Stahl
354K
Problem Set No. 11b
Due Thurday, April 28
1.
Refer to the Game of Chicken in HW11a.
Graph the feasible payoffs, find the
minmax point, and the set of individually rational payoffs.
2.
Infinitely Repeated Chicken
.
Suppose the above game of chicken is played
infinitely often, and both players discounted perperiod payoffs with a
discount factor
δ
∈
(0,1).
Consider the following grim strategy.
Play C in
period 1 and in any period which has a history of everyone playing C.
However, in any period in which someone has played S in the past, play the
mixedstrategy Nash equilibrium of the oneshot game forever thereafter.
(a)
What is the minimum
δ
for which this a subgame perfect Nash equilibrium?
Consider the following strategy.
Play C in period 1.
As long as both
players have used the same action in every past period, play C in the current
period.
If different actions were chosen in some past period, let t* denote the
first such period when the players chose different actions.
Then choose
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 Spring '11
 econ

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