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# ps1 - 14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 1...

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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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ps1 - 14.12 Game Theory Muhamet Yildiz Fall 2005 Homework 1...

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