Decentralized Adaptive Learning : Global Stability inspite of "Local Instability" in a General Equilibrium Example

It is known through an earlier work (Grandmont and Laroque [2]), which analysed discontinuous least squares learning dynamics (around the steady state) in the case of linear temporary equilibrium maps, that there always exists an open cone of initial conditions for which the dynamics are locally divergent. We consider a class of one good overlapping generations models which lead to non-linear temporary equilibrium maps, and the simplest specification ofleast squares learning, to obtain the same local divergence result (around the Golden Rule) but show global convergence of prices to the Golden Rule value. These seemingly contradictory results can be reconciled by observing that the dynamics with learning are non-differentiable at the steady state.