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Machine learning for dynamic incentive problems

Author

Listed:
  • Philipp Renner
  • Simon Scheidegger

Abstract

We propose a generic method for solving infinite-horizon, discrete-time dynamic incentive problems with hidden states. We first combine set-valued dynamic programming techniques with Bayesian Gaussian mixture models to determine irregularly shaped equilibrium value correspondences. Second, we generate training data from those pre-computed feasible sets to recursively solve the dynamic incentive problem by a massively parallelized Gaussian process machine learning algorithm. This combination enables us to analyze models of a complexity that was previously considered to be intractable. To demonstrate the broad applicability of our framework, we compute solutions for models of repeated agency with history dependence, many types, and varying preferences.

Suggested Citation

  • Philipp Renner & Simon Scheidegger, 2017. "Machine learning for dynamic incentive problems," Working Papers 203620397, Lancaster University Management School, Economics Department.
  • Handle: RePEc:lan:wpaper:203620397
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    File URL: http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/working-papers/LancasterWP2017_027.pdf
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    References listed on IDEAS

    as
    1. Sevin Yeltekin & Chris Sleet, 2000. "On The Computation Of Value Correpondences Of Dynamic Games," Computing in Economics and Finance 2000 204, Society for Computational Economics.
    2. Kjetil Storesletten & Chris Telmer & Amir Yaron, 2007. "Asset Pricing with Idiosyncratic Risk and Overlapping Generations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(4), pages 519-548, October.
    3. Tobias Broer & Marek Kapicka & Paul Klein, 2017. "Consumption Risk Sharing with Private Information and Limited Enforcement," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 170-190, January.
    4. Krueger, Dirk & Kubler, Felix, 2004. "Computing equilibrium in OLG models with stochastic production," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1411-1436, April.
    5. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    6. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    7. 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.
    8. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    9. Yongyang Cai & Simon Scheidegger & Sevin Yeltekin & Philipp Renner & Kenneth Judd, 2017. "Optimal Dynamic Fiscal Policy with Endogenous Debt Limits," 2017 Meeting Papers 1543, Society for Economic Dynamics.
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    12. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 957-984.
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    More about this item

    Keywords

    Dynamic Contracts; Principal-Agent Model; Dynamic Programming; Machine Learning; Gaussian Processes; High-performance Computing;

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