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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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    1. Gaudet, Gerard & Lasserre, Pierre & Van Long, Ngo, 1998. "Real investment decisions under adjustment costs and asymmetric information," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 71-95, September.
    2. Grossman, Gene M & Helpman, Elhanan, 1994. "Protection for Sale," American Economic Review, American Economic Association, vol. 84(4), pages 833-850, September.
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    4. 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.
    5. Benchekroun, Hassan & van Long, Ngo, 1998. "Efficiency inducing taxation for polluting oligopolists," Journal of Public Economics, Elsevier, vol. 70(2), pages 325-342, November.
    6. 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.
    7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    8. 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.
    9. Dockner, Engelbert & Feichtinger, Gustav & Mehlmann, Alexander, 1989. "Noncooperative solutions for a differential game model of fishery," Journal of Economic Dynamics and Control, Elsevier, vol. 13(1), pages 1-20, January.
    10. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-172, January.
    11. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
    12. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-1175, September.
    13. Gaudet, Gerard & Lassere, Pierre & Long, Ngo Van, 1995. "Optimal Resource Royalties with Unknown and Temporally Independent Extraction Cost Structures," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(3), pages 715-749, August.
    14. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
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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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