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Unformatted text preview: Economics/Mathematics C103: Introduction to Mathematical Economics Study questions for midterm 1. Consider a setting with 3 bidders and COMPLETE information where bidders values are v 1 > v 2 > v 3 . There is a sealedbid auction where the highest bidder wins the object and pays the AVERAGE of the all three bids. In the case of a tie, the lowestindexed of the high bidders wins the auction and pays the average. (a) Is truthtelling a Nash equilibrium always, never, or sometimes [i.e. for some values ( v 1 ,v 2 ,v 3 ), but not for others] in this game? (b) Prove that there exists a Nash equilibrium where bidder 1 wins the object and pays v 1 . (c) Prove that there can exist (for certain values) a Nash equilibrium where bidder 3 wins the object. 2. The following describes a game with incomplete information: N = { 1 , 2 } ; for each player i = 1 , 2, A i = { F,S } and X i = [0 , 1]. Suppose f ( x 1 ,x 2 ) = 1. We interpret the action F as fight and the action S as surrender, while the signal...
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 Spring '08
 mcfadden
 Economics

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