Generalized Principal-Agent Problem with a Learning Agent
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912661188378624 |
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| author | Lin, Tao Chen, Yiling |
| author_facet | Lin, Tao Chen, Yiling |
| contents | In classic principal-agent problems such as Stackelberg games, contract design, and Bayesian persuasion, the agent best responds 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 problem where the agent approximately best responds, and prove that: (1) If the agent uses contextual no-regret learning algorithms with regret $\mathrm{Reg}(T)$, then the principal can guarantee utility at least $U^* - Θ\big(\sqrt{\tfrac{\mathrm{Reg}(T)}{T}}\big)$, 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 $U^* + O(\frac{\mathrm{SReg(T)}}{T})$. (3) In addition, 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 works on 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Principal-Agent Problem with a Learning Agent Lin, Tao Chen, Yiling Computer Science and Game Theory Artificial Intelligence Machine Learning Theoretical Economics In classic principal-agent problems such as Stackelberg games, contract design, and Bayesian persuasion, the agent best responds 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 problem where the agent approximately best responds, and prove that: (1) If the agent uses contextual no-regret learning algorithms with regret $\mathrm{Reg}(T)$, then the principal can guarantee utility at least $U^* - Θ\big(\sqrt{\tfrac{\mathrm{Reg}(T)}{T}}\big)$, 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 $U^* + O(\frac{\mathrm{SReg(T)}}{T})$. (3) In addition, 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 works on 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. |
| title | Generalized Principal-Agent Problem with a Learning Agent |
| topic | Computer Science and Game Theory Artificial Intelligence Machine Learning Theoretical Economics |
| url | https://arxiv.org/abs/2402.09721 |