Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting

Esat Doruk Cetemen, Felix Feng and Can Urgun
Additional contact information
Felix Feng: University of Washington
Can Urgun: Princeton University

Working Papers from Princeton University. Economics Department.

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.

Keywords: continuous-time contracting; dynamic inconsistency; renegotiation; extended HJB system; non-atomic games (search for similar items in EconPapers)
JEL-codes: D82 D86 D91 (search for similar items in EconPapers)
Date: 2021-02
New Economics Papers: this item is included in nep-gth, nep-mic, nep-ore and nep-upt
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https://scholar.princeton.edu/sites/default/files/tic_01_2021_v41.pdf

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Journal Article: Renegotiation and dynamic inconsistency: Contracting with non-exponential discounting (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:pri:econom:2021-58

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