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A dynamic principal-agent problem as a feedback Stackelberg differential game

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  • Ngo Long
  • Gerhard Sorger

Abstract

We consider situations in which a principal tries to induce an agent to spend effort on accumulating a state variable that affects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg differential game in which the players use feedback strategies. Whereas in general Stackelberg differential games with feedback strategy spaces the leader’s optimization problem has non-standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. A linear-quadratic example is used to illustrate our approach. Copyright Springer-Verlag 2010

Suggested Citation

  • Ngo Long & Gerhard Sorger, 2010. "A dynamic principal-agent problem as a feedback Stackelberg differential game," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 491-509, December.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:4:p:491-509
    DOI: 10.1007/s10100-010-0172-5
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    5. GERARD Gaudet & PIERRE Lasserres & NGO VAN Long, 1996. "Dynamic Incentive Contracts With Uncorrelated Private Information And History-Dependent Outcomes," The Japanese Economic Review, Japanese Economic Association, vol. 47(4), pages 321-334, December.
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    8. Benchekroun, Hassan & Van Long, Ngo, 2002. "On the multiplicity of efficiency-inducing tax rules," Economics Letters, Elsevier, vol. 76(3), pages 331-336, August.
    9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    10. Koji Shimomura & Danyang Xie, 2008. "Advances on Stackelberg open‐loop and feedback strategies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(1), pages 115-133, March.
    11. Benchekroun, Hassan & van Long, Ngo, 1998. "Efficiency inducing taxation for polluting oligopolists," Journal of Public Economics, Elsevier, vol. 70(2), pages 325-342, November.
    12. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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    Citations

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    Cited by:

    1. Kenji Fujiwara & Ngo Long, 2011. "Welfare Implications of Leadership in a Resource Market under Bilateral Monopoly," Dynamic Games and Applications, Springer, vol. 1(4), pages 479-497, December.
    2. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    3. Christopher W. Miller & Insoon Yang, 2015. "Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach," Papers 1506.05497, arXiv.org.
    4. Kenji Fujiwara & Ngo Van Long, 2012. "Optimal Tariffs On Exhaustible Resources: The Case Of Quantity-Setting," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 1-17.
    5. Richard Hartl & Ulrike Leopold-Wildburger & Marion Rauner & Gerhard Sorger & Gernot Tragler & Vladimir Veliov, 2010. "Editorial “In honor of Gustav Feichtinger”," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 433-435, December.
    6. Kenji Fujiwara & Ngo Van Long, 2012. "Optimal Tariffs on Exhaustible Resources: The Case of a Quantity Setting Cartel," CESifo Working Paper Series 3721, CESifo.
    7. Jiarui Gan & Minbiao Han & Jibang Wu & Haifeng Xu, 2023. "Robust Stackelberg Equilibria," Papers 2304.14990, arXiv.org, revised Oct 2023.
    8. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.

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    More about this item

    Keywords

    Differential game; Principal-agent model; Feedback strategies; Stackelberg equilibrium; C61; C73; D82;
    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

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