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Stability of competitive equilibrium with respect to recursive and learning processes. (English) Zbl 0852.90037

Summary: We study the stability of competitive equilibria for recursive processes considered in the learning literature. We define \(h\)-stability (resp. \(F\)-stability, resp. \(\infty\)-stability) to mean stability for the least squares \(h\)-process (resp. \(h\)-stability for some finite \(h\), resp. with respect to the infinite least squares learning process). We show that \(h\)-stability implies \(h'\)-stability for \(h< h'\), with \(h'\) being either finite or infinite. \(F\)-stability implies \(\infty\)-stability, but is not equivalent to it. These results imply that equilibria featuring small income effects and equilibria where goods are gross substitutes are \(h\)-stable for any \(h\) since they are already known to be expectationally stable.

MSC:

91B62 Economic growth models
91E40 Memory and learning in psychology
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