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Unformatted text preview: es and plays Lion his
present payoﬀ is 0 + 3δ/(1 − δ). Hence, player 1 does not want to deviate. We can easily see that
player 2 also does not want to deviate in the P1 mode. If he plays Lion his present value payoﬀ
is 4 + 3δ/(1 − δ ), while if he deviates and plays chicken his present value payoﬀ is 3 + 3δ/(1 − δ ).
3) Consider the inﬁnitely repeated game with the following stage game (Linear Bertrand
duopoly). Simultaneously, Firms 1 and 2 choose prices p1 ∈ [0, 1] and p2 ∈ [0, 1], respectively.
Firm i sells
if pi < pj
⎨ 1 − pi
(1 − pi ) /2 if pi = pj
qi (p1 , p2 ) =
if pi > pj units at price pi , obtaining the stage payoﬀ of pi qi (p1 , p2 ). (All the previous prices are observed,
and each player maximizes the discounted sum of his stage payoﬀs with discount factor δ ∈ (0, 1).)
For each strategy proﬁle below, ﬁnd the range of parameters under which the strategy proﬁle is a
a) (10 points) They both char...
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- Fall '04
- Game Theory