Naivete about temptation and self-control: Foundations for recursive naive quasi-hyperbolic discounting

We introduce and characterize a recursive model of dynamic choice that accommodates naivete about present bias. While recursive representations are important for infinite-horizon problems, the commonly used Strotz model of time inconsistency presents well-known technical difficulties that preclude such representations. Our model incorporates costly self-control in the sense of Gul and Pesendorfer (2001) to overcome these hurdles. The important novel condition is an axiom for naivete. We first introduce definitions of absolute and comparative naivete for a simple two-period model and show that they correspond to tight parametric restrictions for the costly self-control representation. We then proceed to study preferences in infinite-horizon environments. Incorporating our definition of absolute naivete as an axiom, we characterize a recursive representation of naive quasi-hyperbolic discounting with self-control for an individual who is jointly overoptimistic about her present-bias factor and her ability to exert self-control. We also study comparative statics for differences in naivete across individuals, and we present an extension of our model where naivete diminishes over time.