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Unformatted text preview: w and starts working for Google for wage w, ending the game,
• or rejects the oﬀer w and takes Yahoo’s oﬀer r, working for Yahoo for wage r and ending
the game, • or rejects the oﬀer w and then the negotiation continues. ¯
If the game continues to date t ≤ ∞, then the game ends with zero payoﬀs for both players.
¯
If Alice takes Yahoo’s oﬀer at t < t, then the payoﬀ of Alice is rδ t and the payoﬀ of Google
¯
is 0, where δ ∈ (0, 1). If Alice starts working for Google at t < t for wage w , then Alice’s
t
t
payoﬀ is w δ and Google’s payoﬀ is (π − w ) δ , where
π /2 < r < π .
(Note that she cannot work for both Yahoo and Google.)
4 ¯
(a) (10 points) Compute the subgame perfect equilibrium for t = 4. (There are four rounds
of bargaining.) ANSWER: • (2.5pts) Consider t = 3. Alice will get w if she accepts Google, r if she accepts
Yahoo, and 0 if she rejects and continues. Thus, she must choose Google if w ≥ r
sA,3 =
Y ahoo otherwi...
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This document was uploaded on 03/21/2014 for the course ECON 14.12 at MIT.
 Fall '04
 MuhametYildiz
 Game Theory

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