Risk, Delay, and Convex Self-Control Costs

The dual-self model supposes that decision-making involves a conflict between the desire for immediate and safe gratification on the one hand, and riskier long term benefits on the other. This conflict is resolved through a decision criterion that puts weights on both desires. A key element of the model is that this weighting is endogenous, and that changes in constraints that have the same effect on the weights are predicted to lead to the same decisions. The model is consistent with “paradoxes” such as small stakes risk aversion, the common-consequence and common-ratio versions of the Allais paradox, and preference reversals for delayed rewards. It also is consistent with lesser known experimental puzzles, including the effect of reducing the probability of reward on preference reversals induced by delayed rewards, the consequence of delaying rewards for Allais-type preference reversals, preferences for randomization, and reversals due to cognitive load. In Fudenberg and Levine (2006) we used evidence about cognitive load to argue that the cost of self-control is convex and not linear. In this paper our first goal is to