midterm2 2008 solutions

Note that r w2 1 2 r r 1 2 1 1 since

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Unformatted text preview: se. Given this, Google gets 0 if w < r and π − w if w ≥ r. Therefore, it must choose w3 = r. • (2.5pts) Consider t = 2. Google will get π − w if it accepts an offer w by Alice and π − w3 next day if it rejects the offer. Hence Google must Accept iff (π − w) ≥ δ (π − w3 ) i.e. w ≤ π (1 − δ ) + δ r. The best reply for Alice is to offer w2 = π (1 − δ ) + δr. • (2.5pts) [This is the most important step. Disturbingly, the majority of the students failed at this step.] Consider t = 1. Consider Alice’s decision. Alice will get w if she accepts Google, r if she accepts Yahoo, and δ w2 if she rejects and continues. We nned to check whether she prefers Yahoo’s offer to continuing. Note that r > δ w2 = π δ (1 − δ ) + δ 2 r ⇐⇒ r > π δ (1 − δ ) πδ = . 2 1+δ 1−δ Since r > π /2 > 1πδδ , this implies that r > δ w2 . That is, Alice prefers Yahoo’s offer + to continuing, and hence she will never reject and continue. Therefore,...
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