MidtermReviewQuestion

MidtermReviewQuestion - Economics/Mathematics C103:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 sealed-bid auction where the highest bidder wins the object and pays the AVERAGE of the all three bids. In the case of a tie, the lowest-indexed of the high bidders wins the auction and pays the average. (a) Is truth-telling 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...
View Full Document

Ask a homework question - tutors are online