On No-Regret Learning, Fictitious Play, and Nash Equilibrium

This paper addresses the question what is the outcome of multi-agent learning via no-regret algorithms in repeated games? Speci cally, can the outcome of no-regret learning be characterized by traditional game-theoretic solution concepts, such as Nash equilibrium? The conclusion of this study is that no-regret learning is reminiscent of ctitious play: play converges to Nash equilibrium in dominancesolvable, constant-sum, and generalsum 2 2 games, but cycles exponentially in the Shapley game. Notably, however, the information required of ctitious play far exceeds that of noregret learning.