http://www.pnas.org/content/early/2013/01/03/1109672110

It’s a study of the behavior of learning algorithms playing 2-player games in which the number of possible choices is not small but large. The resulting outcomes are typically highly non-stationary, as each player attempts but fails to learn the behavior of the other. It suggests that,for many real world games where players face many choices the outcomes are quite unlikely to be equilibria of any sort.

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W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510.

S. Ishikawa. “Fixed points by a new iteration method.” Proceedings of the American Mathematical Society 44, no. 1 (1974): 147-150.

]]>I have never heard of a debate on the subject. And as I am not an economist, I do not know why economists prefer exact equilibria in discounted games to uniform equilibria. Each model poses different theoretical difficulties, and so they are both challenging to work on. ]]>

Dear Eilon, why do (most) economists not quite accept the notion of (\epsilon)-uniform equilibrium? Rather, most of recent literatures on supergames are about the limit of (exact)-discounted equilibrium payoff set?

Was there ever a debate in history and how was ended? It seems that the situation is rather embarrassing: economists and game theorists are separated from each other, and are doing research (on repeated games) with different notations: compare with the two books of Repeated games by MSZ and Samuelson & Mailath.

It’s abnormal in science.

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