Intertemporal choice and the magnitude effect

A robust finding in experiments on time preference is the magnitude effect: subjects tend to be more patient towards larger rewards. Using a calibration theorem, we argue against standard curvature-based explanations for the finding. We axiomatize a model of preferences over dated rewards that generalizes the standard exponential discounting model by permitting the discount factor to depend on the reward being discounted. The model is shown to behaviorally subsume the hyperbolic discounting model as a special case. When embedded in a sequential bargaining game the model gives rise to multiple stationary subgame perfect equilibria. There may exist equilibria in which the first mover gets a smaller share despite also being the more patient player.