Multiple solutions under quasi-exponential discounting

N. VIEILLE, J. Weibull

Economic Theory

June 2009, vol. 39, n°3, pp.513-526

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

Keywords: Time-consistency, Hyperbolic discounting, Stochastic dynamic programming, Multiplicity, Uniqueness

Infinite horizon dynamic optimization problems with non-exponential time preferences may not only exhibit time inconsistency but may also have multiple solutions with distinct payoffs. We here show that such multiplicity is generic in the sense that it occurs in an open set of such decision problems, even with small state- and action-spaces. Non-exponential discounting allows for an 'addictive' equilibrium alongside a 'virtuous' equilibrium. We also provide a sufficient condition for uniqueness in infinitely repeated decision problems with general action spaces.