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Recursive Methods for Incentive Problems

Author

Listed:
  • Matthias Messner

    (Universita Bocconi)

  • Nicola Pavoni

    (University College London)

  • Christopher Sleet

    (Carnegie Mellon University)

Abstract

Many dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be convergent to the true value function. (Copyright: Elsevier)

Suggested Citation

  • Matthias Messner & Nicola Pavoni & Christopher Sleet, 2012. "Recursive Methods for Incentive Problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 501-525, October.
    • Handle: RePEc:red:issued:12-24
    DOI: 10.1016/j.red.2012.07.002
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    References listed on IDEAS

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    2. Albert Marcet & Ramon Marimon, 2019. "Recursive Contracts," Econometrica, Econometric Society, vol. 87(5), pages 1589-1631, September.
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    8. Harold Cole & Felix Kubler, 2012. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 479-500, October.
    9. Arpad Abraham & Nicola Pavoni, 2008. "Efficient Allocations with Moral Hazard and Hidden Borrowing and Lending: A Recursive Formulation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(4), pages 781-803, October.
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    1. Marimon, Ramon & Werner, Jan, 2021. "The envelope theorem, Euler and Bellman equations, without differentiability," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Messner Matthias & Pavoni Nicola & Sleet Christopher, "undated". "On the Dual Approach to Recursive Optimization," GSIA Working Papers 2012-E12, Carnegie Mellon University, Tepper School of Business.
    3. Neele Balke & Thibaut Lamadon, 2020. "Productivity Shocks, Long-Term Contracts and Earnings Dynamics," NBER Working Papers 28060, National Bureau of Economic Research, Inc.
    4. Alexandros Theloudis & Jorge Velilla & Pierre-André Chiappori & J. Ignacio Gimenéz-Nadal & José Alberto Molina, 2022. "Commitment and the Dynamics of Household Labor Supply," Working Papers 2022-042, Human Capital and Economic Opportunity Working Group.
    5. Miao, Jianjun & Zhang, Yuzhe, 2015. "A duality approach to continuous-time contracting problems with limited commitment," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 929-988.
    6. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    7. Harold Cole & Felix Kubler, 2012. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(4), pages 479-500, October.
    8. Emilio Espino & Julian Kozlowski & Juan M. Sanchez, 2013. "Too big to cheat: Efficiency and Investment in Partnerships," Working Papers 2013-001, Federal Reserve Bank of St. Louis.
    9. 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.
    10. Thibaut Lamadon, 2014. "Productivity Shocks, Dynamic Contracts and Income Uncertainty," 2014 Meeting Papers 243, Society for Economic Dynamics.
    11. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    12. Jean Guillaume Forand & Jan Zapal, 2017. "The Demand and Supply of Favours in Dynamic Relationships," Working Papers 1705, University of Waterloo, Department of Economics, revised Sep 2017.
    13. Gaetano Bloise & Paolo Siconolfi, 2022. "A Negishi Approach to Recursive Contracts," Econometrica, Econometric Society, vol. 90(6), pages 2821-2855, November.
    14. YiLi Chien & Harold L. Cole & Hanno Lustig, 2014. "Implications of heterogeneity in preferences, beliefs and asset trading technologies for the macroeconomy," Working Papers 2014-14, Federal Reserve Bank of St. Louis.
    15. Espino, Emilio & Kozlowski, Julian & Sánchez, Juan M., 2018. "Investment and bilateral insurance," Journal of Economic Theory, Elsevier, vol. 176(C), pages 311-341.
    16. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    17. Matthias Messner & Nicola Pavoni & Christopher Sleet, "undated". "Contractive Dual Methods for Incentive Problems," GSIA Working Papers 2012-E26, Carnegie Mellon University, Tepper School of Business.
    18. Yili Chien & Harold Cole & Hanno Lustig, 2016. "Implications of Heterogeneity in Preferences, Beliefs and Asset Trading Technologies in an Endowment Economy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 215-239, April.
    19. Clayton, Christopher & Schaab, Andreas, 2022. "A Theory of Dynamic Inflation Targets," TSE Working Papers 22-1389, Toulouse School of Economics (TSE).
    20. Kam, Timothy & Stauber, Ronald, 2016. "Solving dynamic public insurance games with endogenous agent distributions: Theory and computational approximation," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 77-98.
    21. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
    22. Balke, Neele & Lamadon, Thibaut, 2021. "Productivity shocks, long-term contracts and earnings dynamics," Working Paper Series 2021:19, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    23. Jaime Hurtubia Torres & Jutta Neitzel, 2017. "Dependency traps in self-targeting food aid programs," Review of Development Economics, Wiley Blackwell, vol. 21(4), pages 147-174, November.
    24. Arie, Guy, 2016. "Dynamic costs and moral hazard: A duality-based approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 1-50.
    25. Charles Brendon, 2011. "Applying perturbation analysis to dynamic optimal tax problems," Economics Series Working Papers 581, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Dynamic contracts; Duality; Dynamic programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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