A counter-example to Karlin's strong conjecture for fictitious play
Author(s)
Pan, Qinxuan![Thumbnail](/bitstream/handle/1721.1/100688/933249721-MIT.pdf.jpg?sequence=3&isAllowed=y)
DownloadFull printable version (286.3Kb)
Other Contributors
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Advisor
Konstantinos Daskalakis.
Terms of use
Metadata
Show full item recordAbstract
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).
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. Cataloged from student-submitted PDF version of thesis. Includes bibliographical references (pages 23-26).
Date issued
2015Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer SciencePublisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science.