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Unformatted text preview: Econ 465 Midterm I Solutions 1. Two people enter a bus. Two adjacent cramped seats are free. Each person must decide whether to sit or stand. Sitting alone is more comfortable than sitting next to the other person, which is more com- fortable than standing. (a) Let the comfort when sitting alone be 3, the comfort when sit- ting adjacent be 2, and the comfort when standing be 1. When selfish, the normal form will be Sit Stand Sit (2,2) (3,1) Stand (1,3) (1,1) Note that Sit is strictly dominant. In this case the only Nash equilibrium is (Sit,Sit). (b) When altruistic, the normal form will be Sit Stand Sit (2,2) (1,3) Stand (3,1) (1,1) Now you payoff is the comfort of the other player, so you are happiest when you stand and he sits. Sit is no longer strictly dominant; in fact, Stand is now Weakly Dominant. There are 3 Pure Strategy Nash equilibria: (Stand, Sit), (Sit, Stand), and (Stand, Stand). Note, some students may demonstrate an answer to part (b) like this: Sit Stand Sit (2,2) (0,3) Stand (3,0) (1,1) That is, they may set up a classic prisoner’s dilemma; There was a problem in the textbook where this was the correct answer, and it wasn’t my intention to trip them up on that. So if they 1 use this for their answer to part (b), and subsequently for part (c), they can have full credit....
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- Spring '08
- Game Theory, Nash, stand, preferred candidate, Sit Stand Sit