Adaptive and Sophisticated Learning in Normal Form Games*

In a class of games including some Cournot and Bertrand games, a sequence of plays converges to the unique Nash equilibrium if and only if the sequence is “consistent with adaptive learning” according to the new definition we propose. In the Arrow-Debreu model with gross substitutes, a sequence of prices converges to the competitive equilibrium if and only if the sequence is consistent with adaptive learning by price-setting market makers for the individual goods. Similar results are obtained for “sophisticated” learning. All the familiar learning algorithms generate play that is consistent with adaptive learning. Jotuntrl r?f EUP nornic Literuture Classification Numbers: 026. 021. c 1991 Academic Pm\\. Inc.