Naiveté about temptation and self-control : foundations for naïve quasi-hyperbolic discounting

We introduce and characterize a recursive model of dynamic choice that accommodates naivete about present bias. The model incorporates costly self-control in the sense of Gul and Pesendorfer (2001) to overcome the technical hurdles of the Strotz representation. The important novel condition is an axiom for naivete. We first introduce appropriate definitions of absolute and comparative naivete for a simple two-period model, and explore their implications for the costly self-control model. We then extend this definition for infinite-horizon environments, and discuss some of the subtleties involved with the extension. Incorporating the 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 resist instant gratification. We study the implications of our proposed comparison of naivete for the parameters of the recursive representation. Finally, we discuss the obstacles that preclude more general notions of naivete, and illuminate the impossibility of a definition that simultaneously incorporates both random choice and costly self-control