A Counter-example to Karlin's Strong Conjecture for Fictitious Play
Author(s)Pan, Qinxuan; Daskalakis, Konstantinos
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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[superscript -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 × n identity matrix, fictitious play may converge (for some tie-breaking) at rate as slow as Ω(t[superscript -1/n]).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
Institute of Electrical and Electronics Engineers (IEEE)
Daskalakis, Constantinos, and Qinxuan Pan. “A Counter-Example to Karlin’s Strong Conjecture for Fictitious Play.” 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (October 2014).
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