14.12 Game Theory
Muhamet Yildiz
Fall 2005
Homework 1
Due on 9/28/2005 (in class)
1. Alice is visiting New York. She calls her friend Bob, who lives in New Haven, from
a pay phone, and they decide that Bob comes to New York and they meet at the
train station. Before they can clarify which train station, Bob’s cell phone’s battery
dies, and they can no longer communicate. Unfortunately, there are two trains from
New Haven to New York: Amtrak, which arrives at the Penn Station, and MetroLiner,
which arrives at the Grand Central, both arriving at noon. Clearly, Bob may take
Amtrak, MetroLiner, or give up and stay home. Alice may check either of the stations
(but not both). It is commonly known among them that they are both expected utility
maximizers and that the following about their preferences are true. They are indi
f
erent
between Bob taking Amtrak while Alice checking the Grand Central and Bob taking
MetroLiner while Alice waiting at the Penn Station. That is, missing each other is
equally bad. Alice is also indi
f
erent between where they meet. For Alice, waiting at
the Penn Station while Bob stays home is as bad as missing each other. But she would
feel worse if she waits at the Grand Central and Bob stays home. In particular, Alice’s
preferences are such that, if she assigns probabilities
p
,
q
,
r
,toAm
trak
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 Spring '05
 MuhammadYildiz
 Game Theory, Alice, Penn Station, best declared position

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