slide35-nov28

slide35-nov28 - ECON 401 Auction Siyang Xiong Rice...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
ECON 401: Auction Siyang Xiong Rice University November 28, 2011 Xiong (Rice University) ECON 401 November 28, 2011 1 / 11
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
auction with reserve price: second-price auction consider two bidders, and bidders&values are i.i.d. distributed uniformly on [0,1]; each bidder takes the following bidding strategy is a BNE. b II . v i / D & bid v i I if v i & r , bid 0 (or do not bid); if v i < r . with this bidding strategy pro±le, what is the expected revenue? Z v 2 D r v 2 D 0 Z v 1 D r v 1 D 0 0 dF . v 1 / dF . v 2 / C Z v 2 D r v 2 D 0 Z v 1 D 1 v 1 D r rdF . v 1 / dF . v 2 / C Z v 1 D r v 1 D 0 Z v 2 D 1 v 2 D r rdF . v 2 / dF . v 1 / C Z v 2 D 1 v 2 D r Z v 1 D 1 v 1 D v 2 v 2 dF . v 1 / dF . v 2 / C Z v 1 D 1 v 1 D r Z v 2 D 1 v 2 D v 1 v 1 dF . v 2 / dF . v 1 / Xiong (Rice University) ECON 401 November 28, 2011 2 / 11
Background image of page 2
auction with reserve price: second-price auction with this bidding strategy pro&le, what is the expected revenue? Z v 2 D r v 2 D 0 Z v 1 D 1 v 1 D r rdF . v 1 / dF . v 2 / D Z v 1 D r v 1 D 0 Z v 2 D 1 v 2 D r rdF . v 2 / dF . v 1 / D Z v 1 D r v 1 D 0 r . 1 & r / dF . v 1 / D r 2 . 1 & r / Z v 2 D 1 v 2 D r Z v 1 D 1 v 1 D v 2 v 2 dF . v 1 / dF . v 2 / D Z v 1 D 1 v 1 D r Z v 2 D 1 v 2 D v 1 v 1 dF . v 2 / dF . v 1 / D Z v 1 D 1 v 1 D r v 1 . 1 & v 1 / dF . v 1 / D " . v 1 / 2 2 & . v 1 / 3 3 # v 1 D 1 v 1 D r D 1 6 & r 2 2 C r 3 3 Xiong (Rice University) ECON 401 November 28, 2011 3 / 11
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
auction with reserve price: second-price auction hence, the expected revenue is 2 r 2 .
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

slide35-nov28 - ECON 401 Auction Siyang Xiong Rice...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online