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Unformatted text preview: Economics 3102
Spring 2009
Professor Jeﬀ Ely Problem Set 7
Due Wednesday May 27
1. Find a mixedstrategy 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 ﬁrstprice auction. Is there a purestrategy Nash equilibirum of the
ﬁrstprice auction? If so, ﬁnd it. If not, show why not.
4. In the Golden Balls game, is the following a mixedstrategy 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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 Spring '08
 Witte
 Economics, Macroeconomics

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