ps4(2010)_v3

# ps4(2010)_v3 - MS&E 246 Game Theory with Engineering...

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MS&E 246: Game Theory with Engineering Applications Feryal Erhun Winter, 2010 Problem Set # 4 Due: February 18, 2010, 5:00 PM outside Terman 305 Reading Assignment: Gibbons, Sections 2.3 and 2.4. 1. (15 pts) Each of n “perfectly rational” individuals, seated around a table, is wearing a hat that is either black or white. Each individual can see the hats of the other n - 1 individuals, but not his own. An observer announces: “Each of you is wearing a hat that is either white or black; at least one of the hats is white. I will start to count slowly. After each number you will have the opportunity to raise a hand. You may do so only when you know the color of your hat.” When, for the first time, will any individual raise his hand? 2. (25 pts, 5 pts for each part) Players 1 and 2 are trying to divide a dollar, which they can consume only after they agree on a division. If they agree on a division that gives x to player 1 and 1 - x to player 2 at date t , then the payoff of player 1 is δ t x , and the payoff to player 2 is δ t (1 - x ), where δ (0 , 1). The dates are t = 0 , 1 , 2 , . . . . If players do not agree by date n , the game automatically ends at the beginning of date n , and each player gets zero payoff.

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