A Geometric Approach to Temptation and Self-Control

Koji Abe

doi:10.4236/tel.2016.63060

Abstract

By making use of a geometry of preferences, Abe (2012) proves the Gul and Pesendorfer’s utility representation theorem about temptation without self-control. This companion paper provides a similar proof for the Gul and Pesendorfer's utility representation theorem about temptation and costly self-control. As a result, the both theorems are proved in the unified way.

Highlights

There is a large and growing literature on temptation and self-control in economics [1] [2]
We provide an alternative proof of the main theorem in [3], that is, the Gul and Pesendorfer’s utility representation theorem about temptation and costly self-control
The proof provides the refined testable implications of the Gul and Pesendorfer model. This geometric approach is taken by the companion paper, [4], to prove the Gul and Pesendorfer’s utility representation theorem about temptation without self-control

Summary

Introduction

There is a large and growing literature on temptation and self-control in economics [1] [2]. We provide an alternative proof of the main theorem in [3], that is, the Gul and Pesendorfer’s utility representation theorem about temptation and costly self-control. We characterize the intuitive notions of temptation and self-control geometrically. We prove the utility representation theorem using the characterization. The proof provides the refined testable implications of the Gul and Pesendorfer model. This geometric approach is taken by the companion paper, [4], to prove the Gul and Pesendorfer’s utility representation theorem about temptation without self-control.

The Gul and Pesendorfer Theorem

A B to avoid succumbing to temptation that is anticipated as follows

Geometry of Temptation and Self-Control

A Geometric Proof for the Gul and Pesendorfer Theorem

Discussion