Econ 200 Problem Set 8 Solution

Econ 200 Problem Set 8 Solution - Answer Key to PS 8 1...

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Unformatted text preview: Answer Key to PS 8 1. Consider a second-price 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, β 1 ( u 1 ) = u for all u 1 ; for bidder 2, β 2 ( u 2 ) = u for all u 2 . What is the seller’s 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 2’s 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) β 1 >u : he wins the auction, pays u , and gets the same utility as bidding β 1 ( u 1 ) = u . ⇒ He is no better o f...
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