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Learning Approximately Optimal Contracts

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  • Alon Cohen
  • Moran Koren
  • Argyrios Deligkas

Abstract

In principal-agent models, a principal offers a contract to an agent to perform a certain task. The agent exerts a level of effort that maximizes her utility. The principal is oblivious to the agent's chosen level of effort, and conditions her wage only on possible outcomes. In this work, we consider a model in which the principal is unaware of the agent's utility and action space: she sequentially offers contracts to identical agents, and observes the resulting outcomes. We present an algorithm for learning the optimal contract under mild assumptions. We bound the number of samples needed for the principal to obtain a contract that is within $\eps$ of her optimal net profit for every $\eps>0$. Our results are robust even when considering risk-averse agents. Furthermore, we show that when there are only two possible outcomes or the agent is risk-neutral, the algorithm's outcome approximates the optimal contract described in the classical theory.

Suggested Citation

  • Alon Cohen & Moran Koren & Argyrios Deligkas, 2018. "Learning Approximately Optimal Contracts," Papers 1811.06736, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:1811.06736
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    References listed on IDEAS

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    1. Noah Williams, 2004. "On Dynamic Principal-Agent Problems in Continuous Time," Levine's Bibliography 122247000000000426, UCLA Department of Economics.
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    3. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
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    5. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    8. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-139, May.
    9. 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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    Cited by:

    1. Banghua Zhu & Sai Praneeth Karimireddy & Jiantao Jiao & Michael I. Jordan, 2023. "Online Learning in a Creator Economy," Papers 2305.11381, arXiv.org.
    2. Guru Guruganesh & Jon Schneider & Joshua Wang & Junyao Zhao, 2023. "The Power of Menus in Contract Design," Papers 2306.12667, arXiv.org.

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