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Unformatted text preview: Answer Key to PS 8 1. Consider a secondprice sealed bid auction. Let u i denote the valuation of bidder i. Let u and u denote the minimum and maximum possible valuations. Suppose there are two bidders. Argue that the following strategies constitute Nash equilibrium: for bidder 1, 1 ( u 1 ) = u for all u 1 ; for bidder 2, 2 ( u 2 ) = u for all u 2 . What is the sellers expected revenue? Can you o f er an argument against these behavior in practice? To show that the above strategies constitute a Nash equilibrium, we need to show that there is no unilateral pro f table deviation for either player. Let us focus on bidder 1, since the case with bidder 2 is entirely symmetric. Given bidder 2s strategy, bidder 1 always wins the auction by bidding u . He pays u for the object. His utility is: u 1 u . Let us consider other bidding strategy for bidder 1. a) 1 >u : he wins the auction, pays u , and gets the same utility as bidding 1 ( u 1 ) = u . He is no better o f...
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.
 Spring '08
 PHILIPHAILE

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