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Optimal Dynamic Contracting: the First-Order Approach and Beyond

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  • Battaglini, Marco
  • Lamba, Rohit
Abstract
We study a dynamic principal-agent model in which the agent's types are serially correlated. In these models, the standard approach consists of first solving a relaxed version in which only local incentive compatibility constraints are considered, and then in proving that the local constraints are sufficient for implementability. We explore the conditions under which this approach is valid and can be used to characterize the profit maximizing contract. We show that the approach works when the optimal allocation in the relaxed problem is monotonic in the types, a condition that is satisfied in most solved examples. Contrary to the static model, however, monotonicity is generally violated in many interesting economic environments. Moreover, when the time horizon is long enough and serial correlation is sufficiently high, global incentive compatibility constraints are generically binding. By fully characterizing a simple two period example, we uncover a number of interesting features of the optimal contract that cannot be observed in spatial environments in which the standard approach works. Finally, we show that even in complex environments, approximately optimal allocations can be easily characterized by focusing on a particular class of contracts in which the allocation is forced to be monotonic.

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  • Battaglini, Marco & Lamba, Rohit, 2015. "Optimal Dynamic Contracting: the First-Order Approach and Beyond," CEPR Discussion Papers 10956, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:10956
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    Cited by:

    1. Garrett, Daniel F., 2017. "Dynamic mechanism design: Dynamic arrivals and changing values," Games and Economic Behavior, Elsevier, vol. 104(C), pages 595-612.
    2. Carlos da Costa & Vitor Farinha Luz, 2018. "The Private Memory of Aggregate Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 169-183, January.
    3. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    4. Karakoç, Gülen & Pagnozzi, Marco & Piccolo, Salvatore, 2022. "The value of transparency in dynamic contracting with entry," International Journal of Industrial Organization, Elsevier, vol. 85(C).
    5. Lu, Jingfeng & Wang, Zijia, 2021. "Optimal selling mechanisms with buyer price search," Journal of Economic Theory, Elsevier, vol. 196(C).
    6. Meng, Dawen & Sun, Lei & Tian, Guoqiang, 2022. "Dynamic mechanism design on social networks," Games and Economic Behavior, Elsevier, vol. 131(C), pages 84-120.
    7. Vitor Farinha Luz, 2022. "Optimal dynamic insurance contracts," Papers 2208.14560, arXiv.org.
    8. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 725-841, Elsevier.
    9. Pham, Hien, 2023. "How Information Design Shapes Optimal Selling Mechanisms," MPRA Paper 120989, University Library of Munich, Germany, revised 06 Mar 2024.
    10. Krasikov, Ilia & Lamba, Rohit, 2021. "A theory of dynamic contracting with financial constraints," Journal of Economic Theory, Elsevier, vol. 193(C).
    11. Terstiege, Stefan, 2016. "Gathering imperfect information before signing a contract," Games and Economic Behavior, Elsevier, vol. 97(C), pages 70-87.
    12. Pham, Hien, 2023. "How Information Design Shapes Optimal Selling Mechanisms," MPRA Paper 120364, University Library of Munich, Germany, revised 06 Mar 2024.
    13. Krähmer, Daniel & Strausz, Roland, 2017. "Sequential versus static screening: An equivalence result," Games and Economic Behavior, Elsevier, vol. 106(C), pages 317-328.
    14. Battaglini, Marco & Lamba, Rohit, 2019. "Optimal dynamic contracting: the first-order approach and beyond," Theoretical Economics, Econometric Society, vol. 14(4), November.
    15. Deb, Rahul & Said, Maher, 2015. "Dynamic screening with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 891-928.
    16. Huiyi Guo & Wei He & Bin Liu, 2022. "Learning by Consuming: Optimal Pricing with Endogenous Information Provision," Papers 2209.01453, arXiv.org.
    17. Dirk Bergemann & Alessandro Pavan, 2015. "Introduction to JET Symposium Issue on "Dynamic Contracts and Mechanism Design"," Cowles Foundation Discussion Papers 2016, Cowles Foundation for Research in Economics, Yale University.
    18. Ilan Lobel & Wenqiang Xiao, 2017. "Technical Note—Optimal Long-Term Supply Contracts with Asymmetric Demand Information," Operations Research, INFORMS, vol. 65(5), pages 1275-1284, October.
    19. Dawen Meng & Guoqiang Tian, 2021. "The competitive and welfare effects of long-term contracts with network externalities and bounded rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 337-375, July.
    20. Chifeng Dai, 2021. "Optimal sequential contract with a risk‐averse supplier," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 92-125, February.
    21. Thomas Mettral, 2018. "Deterministic versus stochastic contracts in a dynamic principal-agent model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 209-218, October.
    22. Pham, Hien, 2023. "How Information Design Shapes Optimal Selling Mechanisms," MPRA Paper 120462, University Library of Munich, Germany, revised 17 Mar 2024.

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    Keywords

    Contract theory; Dynamic contracts;

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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