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Unformatted text preview: she must
choose Google if w ≥ r
sA,1 = sA,3 =
Y ahoo otherwise. Google then must oﬀer w1 = r. • (2.5 pts) Consider t = 0. It must be obvious now that it is the same as t = 2.
Google Accepts iﬀ w ≤ w2 and Alice oﬀers
w0 = w2 = π (1 − δ ) + δ r.
(b) (15 points) Take t = ∞. Conjecture a subgameperfect equilibrium and check that the
conjectured strategy proﬁle is indeed a subgameperfect equilibrium.
ANSWER: From part (a), it is easy to conjecture that the following is a SPE: s∗ : At an odd date Alice accepts an oﬀer w iﬀ w ≥ r, otherwise she takes Yahoo’s
oﬀer. Google oﬀers wG = r. At an even date Alice oﬀers wA = π (1 − δ ) + δ , and
Google accepts an oﬀer w iﬀ w ≤ wA .
5 We use singledeviation principle to check that s∗ is indeed a SPE. There are 4 major
cases two check:
• Consider the case Alice is oﬀered w.
— Suppose that w ≥ wG ≡ r. Alice is supposed to accept and receive w today.
If she deviates by rejecting w and taking Yahoo’s oﬀer, she will get r, which
is not better that w. If she deviates by rejecting and...
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- Fall '04
- Game Theory