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 1949], and shown to converge by [Robinson 1951]. Samuel Karlin conjectured in 1959 that fictitious play converges at rate $O(1/\sqrt{t})$ with the number of steps $t$. We disprove this conjecture showing that, when the payoff matrix of the row player is the $n \times n$ identity matrix, fictitious play may converge with rate as slow as $\Omega(t^{-1/n})$.Comment: 55th IEEE Symposium on Foundations of Computer Scienc

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

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).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).by Qinxuan Pan.M. Eng