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ps2(2010)

# ps2(2010) - 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 # 2 Due: January 28, 2010, 5:00 PM outside Terman 305 Reading Assignment: Gibbons, Chapter 1; and Mas-Colell/Whinston/Green, Sections 7.A, 7.B, 8.A, 8.B, 8.C, 8.D. 1. Consider a simultaneous-move auction in which two players simultaneously choose bids, which must be in nonnegative integer multiples of one cent. The higher bidder wins a dollar bill. If the bids are equal, neither player receives the dollar. Each player must pay his own bid, whether or not he wins the dollar. (The loser pays too.) Each player’s utility is simply his net winnings; that is, the players are risk neutral. Construct a symmetric mixed-strategy equilibrium in which every bid less than 1.00 has a positive probability. 2. One month, a pair of university students decide to download music from a filesharing ser- vice on the Internet. Each student is only allowed a maximum download amount of 100 megabytes. The file server limits the total amount of downloading from the university to

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