Title

Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting

Author(s)

Doruk Cetemen Doruk Cetemen (Collegio Carlo Alberto)

Felix Zhiyu Feng Felix Feng (University of Washington)

Can Urgun Can Urgun (Princeton University)

Abstract

This paper studies a continuous-time, finite-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 difference, a property that is satisfied 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 different from the monotonic action path that would arise under exponential discounting.

Creation Date

2021-02

Section URL ID

Paper Number

2021-58

URL

https://scholar.princeton.edu/sites/default/files/tic_01_2021_v41.pdf

File Function

Jel

D82, D86, D91

Keyword(s)

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

Suppress

false

Series

13