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Generalized Principal-Agent Problem with a Learning Agent

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  • Tao Lin
  • Yiling Chen

Abstract

Classic principal-agent problems such as Stackelberg games, contract design, and Bayesian persuasion, often assume that the agent is able to best respond to the principal's committed strategy. We study repeated generalized principal-agent problems under the assumption that the principal does not have commitment power and the agent uses algorithms to learn to respond to the principal. We reduce this problem to a one-shot generalized principal-agent problem where the agent approximately best responds. Using this reduction, we show that: (1) If the agent uses contextual no-regret learning algorithms with regret $\mathrm{Reg}(T)$, then the principal can guarantee utility at least $U^* - \Theta\big(\sqrt{\tfrac{\mathrm{Reg}(T)}{T}}\big)$, where $U^*$ is the principal's optimal utility in the classic model with a best-responding agent. (2) If the agent uses contextual no-swap-regret learning algorithms with swap-regret $\mathrm{SReg}(T)$, then the principal cannot obtain utility more than $U^* + O(\frac{\mathrm{SReg(T)}}{T})$. But (3) if the agent uses mean-based learning algorithms (which can be no-regret but not no-swap-regret), then the principal can sometimes do significantly better than $U^*$. These results not only refine previous results in Stackelberg games and contract design, but also lead to new results for Bayesian persuasion with a learning agent and all generalized principal-agent problems where the agent does not have private information.

Suggested Citation

  • Tao Lin & Yiling Chen, 2024. "Generalized Principal-Agent Problem with a Learning Agent," Papers 2402.09721, arXiv.org, revised Oct 2024.
  • Handle: RePEc:arx:papers:2402.09721
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    References listed on IDEAS

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    1. Piotr Dworczak & Alessandro Pavan, 2022. "Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion," Econometrica, Econometric Society, vol. 90(5), pages 2017-2051, September.
    2. Colin Camerer, 1998. "Bounded Rationality in Individual Decision Making," Experimental Economics, Springer;Economic Science Association, vol. 1(2), pages 163-183, September.
    3. Jiarui Gan & Minbiao Han & Jibang Wu & Haifeng Xu, 2022. "Generalized Principal-Agency: Contracts, Information, Games and Beyond," Papers 2209.01146, arXiv.org, revised Feb 2024.
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    Cited by:

    1. Tao Lin & Ce Li, 2024. "Information Design with Unknown Prior," Papers 2410.05533, arXiv.org, revised Oct 2024.

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