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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.
r > δ w2 = π δ (1 − δ ) + δ 2 r ⇐⇒ r > π δ (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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- Fall '04
- Game Theory