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Renegotiation and dynamic inconsistency: Contracting with non-exponential discounting

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  • Cetemen, Doruk
  • Feng, Felix Zhiyu
  • Urgun, Can

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 that such an MPE exists, and characterize the optimal contract via an extended Hamilton-Jacobi-Bellman system. We solve the optimal contract in closed-form when discounting is a function of the time-difference only and demonstrate the applicability of the results in several different settings.

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  • Cetemen, Doruk & Feng, Felix Zhiyu & Urgun, Can, 2023. "Renegotiation and dynamic inconsistency: Contracting with non-exponential discounting," Journal of Economic Theory, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jetheo:v:208:y:2023:i:c:s0022053123000029
    DOI: 10.1016/j.jet.2023.105606
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    as
    1. George Loewenstein & Ted O'Donoghue & Matthew Rabin, 2003. "Projection Bias in Predicting Future Utility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(4), pages 1209-1248.
    2. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    3. Wang, Ying & Huang, Wenli & Liu, Bo & Zhang, Xiaohong, 2020. "Optimal effort in the principal-agent problem with time-inconsistent preferences," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    4. Takeuchi, Kan, 2011. "Non-parametric test of time consistency: Present bias and future bias," Games and Economic Behavior, Elsevier, vol. 71(2), pages 456-478, March.
    5. Marina Halac & Pierre Yared, 2014. "Fiscal Rules and Discretion Under Persistent Shocks," Econometrica, Econometric Society, vol. 82, pages 1557-1614, September.
    6. Rey, Patrick & Salanie, Bernard, 1990. "Long-term, Short-term and Renegotiation: On the Value of Commitment in Contracting," Econometrica, Econometric Society, vol. 58(3), pages 597-619, May.
    7. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    8. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    9. Richard H. Thaler & Shlomo Benartzi, 2004. "Save More Tomorrow (TM): Using Behavioral Economics to Increase Employee Saving," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 164-187, February.
    10. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    11. Matthew O. Jackson & Leeat Yariv, 2014. "Present Bias and Collective Dynamic Choice in the Lab," American Economic Review, American Economic Association, vol. 104(12), pages 4184-4204, December.
    12. Peter M. Demarzo & Michael J. Fishman & Zhiguo He & Neng Wang, 2012. "Dynamic Agency and the q Theory of Investment," Journal of Finance, American Finance Association, vol. 67(6), pages 2295-2340, December.
    13. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    14. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    15. Stefano DellaVigna & Ulrike Malmendier, 2004. "Contract Design and Self-Control: Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 353-402.
    16. Zhiguo He & Bin Wei & Jianfeng Yu & Feng Gao, 2017. "Optimal Long-Term Contracting with Learning," The Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2006-2065.
    17. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    18. Wang, Tianxiao & Yong, Jiongmin, 2019. "Backward stochastic Volterra integral equations—Representation of adapted solutions," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4926-4964.
    19. Patrick Bolton & Hui Chen & Neng Wang, 2011. "A Unified Theory of Tobin's q, Corporate Investment, Financing, and Risk Management," Journal of Finance, American Finance Association, vol. 66(5), pages 1545-1578, October.
    20. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    21. B. Douglas Bernheim & Debraj Ray & Şevin Yeltekin, 2015. "Poverty and Self‐Control," Econometrica, Econometric Society, vol. 83(5), pages 1877-1911, September.
    22. Benoit, Jean-Pierre & Krishna, Vijay, 1993. "Renegotiation in Finitely Repeated Games," Econometrica, Econometric Society, vol. 61(2), pages 303-323, March.
    23. Noah Williams, 2011. "Persistent Private Information," Econometrica, Econometric Society, vol. 79(4), pages 1233-1275, July.
    24. Sebastian Gryglewicz & Barney Hartman-Glaser, 2020. "Investment Timing and Incentive Costs," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 309-357.
    25. Paul Heidhues & Botond Koszegi, 2010. "Exploiting Naivete about Self-Control in the Credit Market," American Economic Review, American Economic Association, vol. 100(5), pages 2279-2303, December.
    26. Paul Heidhues & Philipp Strack, 2021. "Identifying Present Bias from the Timing of Choices," American Economic Review, American Economic Association, vol. 111(8), pages 2594-2622, August.
    27. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    28. Ray Debraj, 1994. "Internally Renegotiation-Proof Equilibrium Sets: Limit Behavior with Low Discounting," Games and Economic Behavior, Elsevier, vol. 6(1), pages 162-177, January.
    29. Fudenberg, Drew & Tirole, Jean, 1990. "Moral Hazard and Renegotiation in Agency Contracts," Econometrica, Econometric Society, vol. 58(6), pages 1279-1319, November.
    30. Andrew Caplin & John Leahy, 2001. "Psychological Expected Utility Theory and Anticipatory Feelings," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 55-79.
    31. Coles, Jeffrey L. & Daniel, Naveen D. & Naveen, Lalitha, 2006. "Managerial incentives and risk-taking," Journal of Financial Economics, Elsevier, vol. 79(2), pages 431-468, February.
    32. Alberto Bisin & Alessandro Lizzeri & Leeat Yariv, 2015. "Government Policy with Time Inconsistent Voters," American Economic Review, American Economic Association, vol. 105(6), pages 1711-1737, June.
    33. Loewenstein, George, 1987. "Anticipation and the Valuation of Delayed Consumption," Economic Journal, Royal Economic Society, vol. 97(387), pages 666-684, September.
    34. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    35. Daniel Gottlieb & Xingtan Zhang, 2021. "Long‐Term Contracting With Time‐Inconsistent Agents," Econometrica, Econometric Society, vol. 89(2), pages 793-824, March.
    36. Andrew Caplin & John Leahy, 2004. "The Social Discount Rate," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1257-1268, December.
    37. Philip Bond & Gustav Sigurdsson, 2018. "Commitment Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 194-222.
    38. Simone Galperti, 2015. "Commitment, Flexibility, and Optimal Screening of Time Inconsistency," Econometrica, Econometric Society, vol. 83(4), pages 1425-1465, July.
    39. Daniel Gottlieb, 2008. "Competition over Time‐Inconsistent Consumers," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(4), pages 673-684, August.
    40. Michael D. Grubb, 2015. "Overconfident Consumers in the Marketplace," Journal of Economic Perspectives, American Economic Association, vol. 29(4), pages 9-36, Fall.
    41. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    42. Christopher Harris & David Laibson, 2013. "Instantaneous Gratification," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 205-248.
    43. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    44. Eduardo Faingold & Yuliy Sannikov, 2011. "Reputation in Continuous‐Time Games," Econometrica, Econometric Society, vol. 79(3), pages 773-876, May.
    45. Dan Cao & Iván Werning, 2018. "Saving and Dissaving With Hyperbolic Discounting," Econometrica, Econometric Society, vol. 86(3), pages 805-857, May.
    46. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    47. repec:oup:qjecon:v:128:y:2012:i:1:p:205-248 is not listed on IDEAS
    48. Strulovici, Bruno & Szydlowski, Martin, 2015. "On the smoothness of value functions and the existence of optimal strategies in diffusion models," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1016-1055.
    49. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    50. Ivan Marinovic & Felipe Varas, 2019. "CEO Horizon, Optimal Pay Duration, and the Escalation of Short‐Termism," Journal of Finance, American Finance Association, vol. 74(4), pages 2011-2053, August.
    51. Balder, Erik J, 1991. "On Cournot-Nash Equilibrium Distributions for Games with Differential Information and Discontinuous Payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 339-354, October.
    52. He, Zhiguo, 2011. "A model of dynamic compensation and capital structure," Journal of Financial Economics, Elsevier, vol. 100(2), pages 351-366, May.
    53. Chade, Hector & Prokopovych, Pavlo & Smith, Lones, 2008. "Repeated games with present-biased preferences," Journal of Economic Theory, Elsevier, vol. 139(1), pages 157-175, March.
    54. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    55. li, Hong & Mu, Congming & Yang, Jinqiang, 2016. "Optimal contract theory with time-inconsistent preferences," Economic Modelling, Elsevier, vol. 52(PB), pages 519-530.
    56. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    57. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    58. Liu, Bo & Mu, Congming & Yang, Jinqiang, 2017. "Dynamic agency and investment theory with time-inconsistent preferences," Finance Research Letters, Elsevier, vol. 20(C), pages 88-95.
    59. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    60. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    61. Gonzalo Cisternas, 2018. "Two-Sided Learning and the Ratchet Principle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 307-351.
    62. Feng, Felix Zhiyu & Westerfield, Mark M., 2021. "Dynamic resource allocation with hidden volatility," Journal of Financial Economics, Elsevier, vol. 140(2), pages 560-581.
    63. Matthew O. Jackson & Leeat Yariv, 2015. "Collective Dynamic Choice: The Necessity of Time Inconsistency," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 150-178, November.
    64. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    65. Boualem Djehiche & Minyi Huang, 2016. "A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type," Dynamic Games and Applications, Springer, vol. 6(1), pages 55-81, March.
    66. John Core & Wayne Guay, 2002. "Estimating the Value of Employee Stock Option Portfolios and Their Sensitivities to Price and Volatility," Journal of Accounting Research, Wiley Blackwell, vol. 40(3), pages 613-630, June.
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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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