Stability of competitive equilibrium with respect to recursive and learning processes

We study the stability of competitive equilibria for recursive processes considered in the learning litterature. We define h-stability (resp. F-stability, resp. infinity-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 infinity-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 expectationaly stable. (C) 1996 Academic Press, Inc.