310-2ps7 - Economics 310-2 Spring 2009 Professor Jeff Ely...

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Unformatted text preview: Economics 310-2 Spring 2009 Professor Jeff Ely Problem Set 7 Due Wednesday May 27 1. Find a mixed-strategy Nash equilibrium of the following game. R S P R 0,0 1,-1 -1,1 S -1,1 0,0 1,-1 P 1,-1 -1,1 0,0 2. Two bidders are competing in a Vickrey auction. Bidder 1 has value 13 and bidder 2 has value 8. We know that each bidder has a dominant strategy to bid his value. But we have also seen an example of a game in which there was a Nash equilibrium in which a dominated strategy was played. Find a Nash equilibrium of this Vickrey auction in which bidder 2 wins. 3. Consider the same setting as the previous question (2 bidders, same values) but now consider the first-price auction. Is there a pure-strategy Nash equilibirum of the first-price auction? If so, find it. If not, show why not. 4. In the Golden Balls game, is the following a mixed-strategy Nash equilibrium? Player 1 plays steal with probability 1 and player 2 plays steal with probability .63 and split with probability .37. 1 ...
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