A counter-example to Karlin's strong conjecture for fictitious play

Fictitious play is a natural dynamic for equilibrium play in zero-sum games, proposed by Brown , and shown to converge by Robinson . Samuel Karlin conjectured in 1959 that fictitious play converges at rate O(t- 1/ 2) with respect to the number of steps t. We disprove this conjecture by showing that, when the payoff matrix of the row player is the n x n identity matrix, fictitious play may converge (for some tie-breaking) at rate as slow as [Omega](t- 1/n).

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Pan, Qinxuan

Advisor dc:contributor.advisor

• Konstantinos Daskalakis.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/100688

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/100688