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Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

Author

Listed:
  • Felix Kubler

    (University of Zurich)

  • Harold L. Cole

    (University of Pennsylvania)

Abstract

Marcet and Marimon (1994, revised 1998) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a flat region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through -- one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal's choice set is not convex but where randomization is possible.

Suggested Citation

  • Felix Kubler & Harold L. Cole, 2011. "Recursive Contracts, Lotteries and Weakly Concave Pareto Sets," 2011 Meeting Papers 59, Society for Economic Dynamics.
  • Handle: RePEc:red:sed011:59
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    References listed on IDEAS

    as
    1. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2004. "Aggregate Consequences of Limited Contract Enforceability," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 817-847, August.
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    Citations

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    Cited by:

    1. 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.
    2. Messner Matthias & Pavoni Nicola & Sleet Christopher, "undated". "Recursive Methods for Dynamic Incentive Problems," GSIA Working Papers 2012-E13, Carnegie Mellon University, Tepper School of Business.
    3. Giancarlo Corsetti & Luca Dedola & Francesca Viani, 2012. "The international risk sharing puzzle is at business cycle and lower frequency," Canadian Journal of Economics, Canadian Economics Association, pages 448-471.
    4. Nicola Pavoni & Christopher Sleet & Matthias Messner, 2014. "The Dual Approach to Recursive Optimization: Theory and Examples," 2014 Meeting Papers 1267, Society for Economic Dynamics.
    5. 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.
    6. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    7. 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.
    8. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, Elsevier.
    9. Marcet, A. & Marimon, R., 1998. "Recursive Contracts," Economics Working Papers eco98/37, European University Institute.
    10. 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.
    11. Albert Marcet & Ramon Marimon, 1994. "Recursive contracts," Economics Working Papers 337, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 1998.
    12. Chien, YiLi & Cole, Harold L. & Lustig, Hanno, 2014. "Implications of heterogeneity in preferences, beliefs and asset trading technologies for the macroeconomy," Working Papers 2014-14, Federal Reserve Bank of St. Louis.
    13. 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.
    14. 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.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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