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

49 Pages Posted: 6 Feb 2018

See all articles by David S. Ahn

David S. Ahn

University of California, Berkeley - Department of Economics

Ryota Iijima

Yale University - Cowles Foundation

Todd Sarver

Duke University - Department of Economics

Multiple version iconThere are 3 versions of this paper

Date Written: February 2, 2018

Abstract

We introduce and characterize a recursive model of dynamic choice that accommodates naivete about present bias. While recursive representations are important for tractable analysis of in nite-horizon problems, the commonly-used Strotz model of time inconsistency presents well-known technical difficulties in extensions to dynamic environments. 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 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 develop suitable extensions of these definitions to in nite-horizon environments. 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 also study the implications of our proposed comparison of naivete for this recursive representation and uncover new restrictions on the present-bias and self-control parameters that characterize comparative naivete. Finally, we discuss the subtleties that preclude more general notions of naivete, and illuminate the impossibility of a definition that simultaneously accommodates both random choice and costly self-control.

Keywords: Naive, Sophisticated, Self-control, Quasi-hyperbolic discounting

JEL Classification: D11, D15, D91

Suggested Citation

Ahn, David S. and Iijima, Ryota and Sarver, Todd, Naiveté About Temptation and Self-Control: Foundations for Naive Quasi-Hyperbolic Discounting (February 2, 2018). Cowles Foundation Discussion Paper No. 2099R, Available at SSRN: https://ssrn.com/abstract=3118431 or http://dx.doi.org/10.2139/ssrn.3118431

David S. Ahn

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

Ryota Iijima (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Todd Sarver

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

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