midterm2 2008 solutions

# Suppose that w wg r alice is supposed to accept and

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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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