This paper attemps to identify, in a framework deliberately stripped of unnecessary technical- ities, some of the basic reasons why adaptive learning may or may not lead to stability and convergence to self-fulfilling expectations in large socioeconomic systems where no agent, or collection of agents, can act to manipulate macroeconomic outcomes. It is shown that if agents are somewhat uncertain about the local stability of the system, and are accordingly ready to extrapolate a large range of regularities (trends) that may show up in past small deviations from equilibrium, including divergent ones, the learning dynamics is locally divergent. On the other hand, if agents are fairly sure of the local stability of the system, and extrapolate only convergent trends out of small past deviations from equilibrium, one may get local stability. This “uncertainty principle” does show up in a wide variety of contexts: smooth or discontin- uous, finite or infinite memory learning rules, error learning, recursive least squares, Bayesian learning.

Cet article donne des conditions suffisantes pour que la matrice Jacobienne de la demande concurrentielle agrge soit dfinie ngative.Cette proprit forte implique en particulier que l'axiome faible de la prfrence rvle est satisfait par la demande agrge, et que la demande totale pour chaque bien augmente lorsque son prix dc1'0 i t.Ces cond i tians suffisantes portent sur la distribution des prfrences et sont indpendantes de la distribution des revenus.L'approche repose sur la.notion de transformation homothtique d'une relatiof\de prfrence.On discute galement la porte pour ce type de problme de la notion de transformation affine d'une prfrence, qui introduit une structure algbrique intressante sur l'espace des prfrences.On montre galement comment le rsultat est li celui obenu par W. Hildenbrand (Econometrica (1983)) en posant des restrictions sur la distribution des revenus.

Jean-Michel Grandmont, Guy Laroque; On Temporary Keynesian Equilibria, The Review of Economic Studies, Volume 43, Issue 1, 1 February 1976, Pages 53–67, ht