# A Geometric Approach to Temptation

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## Abstract

We provide a simple geometric proof of the Gul and Pesendorfer’s (Econometrica 69(6):1403–1435, 2001) utility representation theorem about choice under temptation without self-control. We extract two incomplete orders from preferences: temptation relation and resistance relation. We characterize those relations geometrically and obtain temptation utility using a separation method à la Aumann (Econometrica 30(3):445–462, 1962).

## Keywords

Temptation No self-control Temptation utility## Notes

### Acknowledgements

I would like to express my appreciation to Hideo Suehiro for invaluable discussions and encouragement. I would also like to thank Kazuya Hyogo, Hajime Kobayashi, Noriaki Matsushima, Eiichi Miyagawa, Wolfgang Pesendorfer, and Norio Takeoka for their valuable comments and suggestions. Very useful remarks of two anonymous reviewers and the editor have lead to an improved presentation of the results. Responsibility for any remaining errors rests with the author. The addendum part was supported by JSPS KAKENHI Grant Number 24730166.

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