We develop a dual-self model of self-control that is compatible with
modern dynamic macroeconomic theory and evidence. We show that a convex cost of self-control explains a wide range of behavioral anomalies concerning risk, including the Allais paradox, and also
explains the observed interaction between risk and delay. We calibrate the model to obtain a quantitative fit. We find that most of the data can be explained with subjective interest rates in the range of 1-7 percent, short-run relative risk aversion of about two, and a time horizon of one day for the short-run self. (JEL D11, D44, D81)
Fudenberg, Drew, and David K. Levine.
"Risk, Delay, and Convex Self-Control Costs."
American Economic Journal: Microeconomics,
Consumer Economics: Theory
Criteria for Decision-Making under Risk and Uncertainty