Uncoupled Dynamics Do Not Lead to Nash Equilibrium

Sergiu Hart and Andreu Mas-Colell

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(*) For the last sentence in the proof of Lemma 3, consider the three cases: four real eigenvalues; two real eigenvalues and one conjugate pair; two conjugate pairs.

We call a dynamical system uncoupled if the dynamic for each player does not depend on the payoff functions of the other players. We show that there are no uncoupled dynamics that are guaranteed to converge to Nash equilibrium, even when the Nash equilibrium is unique.

Journal of Economic Literature Classification Numbers: C7, D83.

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