Lowest Unique Bid - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T04:30:36Z http://mathoverflow.net/feeds/question/27004 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/27004/lowest-unique-bid Lowest Unique Bid Ricky Demer 2010-06-04T03:52:08Z 2012-02-17T00:10:34Z <p>Each of n players simultaneously choose a positive integer, and one of the players who chose [the least number of [the numbers chosen the fewest times of [the numbers chosen at least once]]] is selected at random and that player wins.</p> <p>For n=3, the symmetric Nash equilibrium is the player chooses m with probability 1/(2^m).</p> <p>What is the symmetric Nash equilibrium for n=4? Is it known for general n?</p> http://mathoverflow.net/questions/27004/lowest-unique-bid/27069#27069 Answer by Timothy Chow for Lowest Unique Bid Timothy Chow 2010-06-04T17:57:12Z 2010-06-04T20:31:37Z <p>There is some published literature on this problem. See for example the following papers and the references therein.</p> <p>Baek and Bernhardsson, <a href="http://arxiv.org/pdf/1001.1065v1" rel="nofollow">Equilibrium solution to the lowest unique positive integer game</a></p> <p>Rapoport et al., <a href="http://mpra.ub.uni-muenchen.de/4185/" rel="nofollow">Unique bid auctions: Equilibrium solutions and experimental evidence</a></p> <p>Ostling et al., <a href="http://en.scientificcommons.org/23204285" rel="nofollow">Strategic thinking and learning in the field and lab: Evidence from Poisson LUPI lottery games</a></p> <p>Houba et al., <a href="http://dare.ubvu.vu.nl//handle/1871/12947" rel="nofollow">The Unique-lowest Sealed-bid Auction</a></p> <p>Apparently, in general, the Nash equilibria are intractable to describe.</p> http://mathoverflow.net/questions/27004/lowest-unique-bid/88675#88675 Answer by Dan Loeb for Lowest Unique Bid Dan Loeb 2012-02-17T00:10:34Z 2012-02-17T00:10:34Z <p>There are non symmetric Nash equilibria. For example with 3 players: (1,1,2) is a silly solution.</p>