General equilibrium dynamics with nai͏̈ve and sophisticated hyperbolic consumers in an overlapping generations economy

Using an overlapping generations model, this paper describes interactions between nai͏̈ve and sophisticated hyperbolic discounters in general equilibrium. The nai͏̈fs, who overestimate their future propensity to save and hence over-forecast the future equilibrium asset prices, are exploited through capital transactions by sophisticates, who correctly forecast the future asset prices by incorporating the nai͏̈fs' mis-forecasts. Due to the capital losses, the nai͏̈fs fall into bankruptcy when they are highly present-biased, highly patient, and small in proportion. Under permissive conditions, the equilibrium is shown to be globally stable and Pareto inefficient in the ex-post sense.