Uncoupled Dynamics Do Not Lead to Nash Equilibrium

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Prediction, learning, and games (2006, background): “On the negative side, Hart and Mas-Colell [148, 149] show that it is impossible to achieve convergence to Nash equilibrium for all games if one is restricted to use stationary strategies that have bounded memory.”
Generalised weakened fictitious play (2006, background): “We note here that Hart and Mas-Colell (2003) prove that no “uncoupled””
Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria (2005, background): “In particular, the paper [ 26 ] shows that a generalized version of the Jordan game will not exhibit convergence for any strategy adjustment mechanism—not just a best response mechanism—provided that players do not share their utility functions and update mechanisms are static functions of empirical”
AWESOME: A general multiagent learning algorithm that converges in self-play and learns a best response against stationary opponents (2003, background): “In any case, a recent result shows that (for continuous-time dynamics) some knowledge of the other players’ payoffs is necessary to converge to Nash equilibrium ( Hart & Mas-Colell, 2003 ).”