Strategizing against No-Regret Learners in First-Price Auctions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916123717402624 |
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| author | Rubinstein, Aviad Zhao, Junyao |
| author_facet | Rubinstein, Aviad Zhao, Junyao |
| contents | We study repeated first-price auctions and general repeated Bayesian games between two players, where one player, the learner, employs a no-regret learning algorithm, and the other player, the optimizer, knowing the learner's algorithm, strategizes to maximize its own utility. For a commonly used class of no-regret learning algorithms called mean-based algorithms, we show that (i) in standard (i.e., full-information) first-price auctions, the optimizer cannot get more than the Stackelberg utility -- a standard benchmark in the literature, but (ii) in Bayesian first-price auctions, there are instances where the optimizer can achieve much higher than the Stackelberg utility.
On the other hand, Mansour et al. (2022) showed that a more sophisticated class of algorithms called no-polytope-swap-regret algorithms are sufficient to cap the optimizer's utility at the Stackelberg utility in any repeated Bayesian game (including Bayesian first-price auctions), and they pose the open question whether no-polytope-swap-regret algorithms are necessary to cap the optimizer's utility. For general Bayesian games, under a reasonable and necessary condition, we prove that no-polytope-swap-regret algorithms are indeed necessary to cap the optimizer's utility and thus answer their open question. For Bayesian first-price auctions, we give a simple improvement of the standard algorithm for minimizing the polytope swap regret by exploiting the structure of Bayesian first-price auctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strategizing against No-Regret Learners in First-Price Auctions Rubinstein, Aviad Zhao, Junyao Computer Science and Game Theory Data Structures and Algorithms Machine Learning We study repeated first-price auctions and general repeated Bayesian games between two players, where one player, the learner, employs a no-regret learning algorithm, and the other player, the optimizer, knowing the learner's algorithm, strategizes to maximize its own utility. For a commonly used class of no-regret learning algorithms called mean-based algorithms, we show that (i) in standard (i.e., full-information) first-price auctions, the optimizer cannot get more than the Stackelberg utility -- a standard benchmark in the literature, but (ii) in Bayesian first-price auctions, there are instances where the optimizer can achieve much higher than the Stackelberg utility. On the other hand, Mansour et al. (2022) showed that a more sophisticated class of algorithms called no-polytope-swap-regret algorithms are sufficient to cap the optimizer's utility at the Stackelberg utility in any repeated Bayesian game (including Bayesian first-price auctions), and they pose the open question whether no-polytope-swap-regret algorithms are necessary to cap the optimizer's utility. For general Bayesian games, under a reasonable and necessary condition, we prove that no-polytope-swap-regret algorithms are indeed necessary to cap the optimizer's utility and thus answer their open question. For Bayesian first-price auctions, we give a simple improvement of the standard algorithm for minimizing the polytope swap regret by exploiting the structure of Bayesian first-price auctions. |
| title | Strategizing against No-Regret Learners in First-Price Auctions |
| topic | Computer Science and Game Theory Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2402.08637 |