# Solution to Exchanges 8.2 puzzle: a Dutch Dutch auction clock auction

Solution to Exchanges 8.2 puzzle: a Dutch Dutch auction clock auction Solution to Exchanges 8.2 Puzzle: A Dutch Dutch Auction Clock Auction ASSAF ROMM The Hebrew University of Jerusalem This is a solution to the editor ™s puzzle from issue 8.2 of SIGecom Exchanges. The puzzle is about nding a Bayesian equilibrium for a Dutch auction which can end according to a stochastic price schedule. The full puzzle [Conitzer 2009] can be found online at: http://www.sigecom.org/exchanges/volume 8/2/puzzle.pdf. Categories and Subject Descriptors: K.4.4 [Computers and Society]: Electronic Commerce General Terms: Economics Additional Key Words and Phrases: Dutch Auction, Stochastic Reserve Price The puzzle asks us to nd a Bayesian equilibrium for a Dutch auction with N bidders, where bidders ™ values are symmetrically and independently distributed on the interval [0, 1].1 Denote by F (x) the cumulative distribution function according to which values are drawn, with f being the corresponding probability density function. The twist is that the object considered for sale is the Dutch auction clock itself, and it might break during the auction process. Let W (p) describe the breaking probability function, i.e. the probability that the auction clock breaks after it reaches price p. If the clock breaks before the auction ends, its value drops to 0 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

# Solution to Exchanges 8.2 puzzle: a Dutch Dutch auction clock auction

, Volume 10 (1) – Mar 1, 2011
5 pages

/lp/association-for-computing-machinery/solution-to-exchanges-8-2-puzzle-a-dutch-dutch-auction-clock-auction-0mC7CmaMtv
Publisher
Association for Computing Machinery
ISSN
1551-9031
DOI
10.1145/1978721.1978732
Publisher site
See Article on Publisher Site

### Abstract

Solution to Exchanges 8.2 Puzzle: A Dutch Dutch Auction Clock Auction ASSAF ROMM The Hebrew University of Jerusalem This is a solution to the editor ™s puzzle from issue 8.2 of SIGecom Exchanges. The puzzle is about nding a Bayesian equilibrium for a Dutch auction which can end according to a stochastic price schedule. The full puzzle [Conitzer 2009] can be found online at: http://www.sigecom.org/exchanges/volume 8/2/puzzle.pdf. Categories and Subject Descriptors: K.4.4 [Computers and Society]: Electronic Commerce General Terms: Economics Additional Key Words and Phrases: Dutch Auction, Stochastic Reserve Price The puzzle asks us to nd a Bayesian equilibrium for a Dutch auction with N bidders, where bidders ™ values are symmetrically and independently distributed on the interval [0, 1].1 Denote by F (x) the cumulative distribution function according to which values are drawn, with f being the corresponding probability density function. The twist is that the object considered for sale is the Dutch auction clock itself, and it might break during the auction process. Let W (p) describe the breaking probability function, i.e. the probability that the auction clock breaks after it reaches price p. If the clock breaks before the auction ends, its value drops to 0

### Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Mar 1, 2011