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Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting

Author

Listed:
  • Doruk Cetemen

    (Collegio Carlo Alberto)

  • Felix Zhiyu Feng

    (University of Washington)

  • 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.

Suggested Citation

  • Doruk Cetemen & Felix Zhiyu Feng & Can Urgun, 2021. "Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting," Working Papers 2021-58, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2021-58
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    More about this item

    Keywords

    continuous-time contracting; dynamic inconsistency; renegotiation; extended HJB system; non-atomic games;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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