Naivet� About Temptation and Self-Control: Foundations for Naive Quasi-Hyperbolic Discounting

We introduce and characterize a recursive model of dynamic choice that accommodates naivet� 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 naivet�. We first introduce appropriate definitions of absolute and comparative naivet� 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 naivet� 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 naivet� for the parameters of the recursive representation. Finally, we discuss the obstacles that preclude more general notions of naivet�, and illuminate the impossibility of a definition that simultaneously incorporates both random choice and costly self-control. devices.