Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting

58 Pages Posted: 25 Aug 2019 Last revised: 1 Feb 2021

See all articles by Doruk Cetemen

Doruk Cetemen

Collegio Carlo Alberto

Felix Zhiyu Feng

University of Washington - Michael G. Foster School of Business

Can Urgun

Northwestern University - Kellogg School of Management

Date Written: February 1, 2021

Abstract

This paper studies a continuous-time, nite-horizon contracting problem with renegotiation
and dynamic inconsistency arising from non-exponential discounting. The
problem is formulated as a dynamic game played among the agent, the principal and
their respective future "selves", each with their own discount function. We identify
the principal optimal renegotiation-proof contract as a Markov Perfect Equilibrium
(MPE) of the game, prove such a MPE exists, and characterize the optimal contract
via an extended Hamilton-Jacobi-Bellman system. We solve the optimal contract in
closed form when the discount functions of the selves are related by time di erence,
a property that is satis ed by common forms of non-exponential discounting such as
quasi-hyperbolic discounting and anticipatory utility. In particular, quasi-hyperbolic
discounting leads to a U-shaped action path and anticipatory utility leads to a humshaped
path, both are qualitatively di erent from the monotonic action path that
would arise under exponential discounting.

Keywords: continuous-time contracting, dynamic inconsistency, renegotiation, extended HJB system, non-atomic games

JEL Classification: D81, D86, D91

Suggested Citation

Cetemen, Doruk and Feng, Felix and Urgun, Can, Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting (February 1, 2021). Available at SSRN: https://ssrn.com/abstract=3442367 or http://dx.doi.org/10.2139/ssrn.3442367

Doruk Cetemen

Collegio Carlo Alberto

Piazza Arbarello 8, Torino
Torino, Torino 10122
Italy
+39 011 670 5000 (Phone)
+39 011 670 5082 (Fax)

HOME PAGE: http://https://www.carloalberto.org/

Felix Feng (Contact Author)

University of Washington - Michael G. Foster School of Business ( email )

Box 353200
Seattle, WA 98195-3200
United States

Can Urgun

Northwestern University - Kellogg School of Management

2001 Sheridan Road
Evanston, IL 60208
United States

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