mlsanityData to 7 Oct 2026

Strategizing against Learners in Bayesian Games

arXiv 2205.08562 ↗First posted 17 May 2022cs.LG cs.GTcited by 33

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Abstract (arXiv)

We study repeated two-player games where one of the players, the learner, employs a no-regret learning strategy, while the other, the optimizer, is a rational utility maximizer. We consider general Bayesian games, where the payoffs of both the optimizer and the learner could depend on the type, which is drawn from a publicly known distribution, but revealed privately to the learner. We address the following questions: (a) what is the bare minimum that the optimizer can guarantee to obtain regardless of the no-regret learning algorithm employed by the learner? (b) are there learning algorithms that cap the optimizer payoff at this minimum? (c) can these algorithms be implemented efficiently? While building this theory of optimizer-learner interactions, we define a new combinatorial notion of regret called polytope swap regret, that could be of independent interest in other settings.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 5 of its 23 references that are in the map. First posted on arXiv 17 May 2022.

Builds on

5 of 23 references.

References · 5

  1. 2019Strategizing against No-regret Learnerscited by 48
  2. 2017Selling to a No-Regret Buyercited by 43
  3. 2020Contracts under Moral Hazard and Adverse Selectioncited by 21
  4. 2017On Stackelberg Mixed Strategiescited by 10
  5. 2018Robust Repeated Auctions under Heterogeneous Buyer Behaviorcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 7; 2024: 9; 2025: 10; 2026: 6.

33 papers.

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  1. 2023U-Calibration: Forecasting for an Unknown Agentcited by 46
  2. 2023Fast swap regret minimization and applications to approximate correlated equilibriacited by 30
  3. 2023Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agentscited by 25
  4. 2024Contracting with a Learning Agentcited by 22
  5. 2023Is Learning in Games Good for the Learners?cited by 19
  6. 2025Full Swap Regret and Discretized Calibrationcited by 13
  7. 2024Strategizing against No-Regret Learners in First-Price Auctionscited by 8
  8. 2023Persuading a Behavioral Agent: Approximately Best Responding and Learningcited by 7
  9. 2024Strategically-Robust Learning Algorithms for Bidding in First-Price Auctionscited by 7
  10. 2024Maximizing utility in multi-agent environments by anticipating the behavior of other learnerscited by 7
  11. 2025Swap Regret and Correlated Equilibria Beyond Normal-Form Gamescited by 7
  12. 2023Pseudonorm Approachability and Applications to Regret Minimizationcited by 5
21 more
  1. 2024Generalized Principal-Agent Problem with a Learning Agentcited by 5
  2. 2024Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactionscited by 5
  3. 2025Emergent Risk Awareness in Rational Agents under Resource Constraintscited by 5
  4. 2025Should Decision-Makers Reveal Classifiers in Online Strategic Classification?cited by 5
  5. 2024Rate-Preserving Reductions for Blackwell Approachabilitycited by 4
  6. 2023Smooth Nash Equilibria: Algorithms and Complexitycited by 3
  7. 2024Games with Payments between Learning Agentscited by 3
  8. 2024Learning to Play Against Unknown Opponentscited by 3
  9. 2025Learning and Computation of Phi-Equilibria at the Frontier of Tractabilitycited by 3
  10. 2026An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to Phi-Regret Minimizationcited by 3
  11. 2025Computational Intractability of Strategizing against Online Learnerscited by 2
  12. 2026Swap Regret Minimization Through Response-Based Approachabilitycited by 2
  13. 2026Near-optimal Swap Regret Minimization for Convex Lossescited by 2
  14. 2025Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learnerscited by 1
  15. 2025Best of Both Worlds: Regret Minimization versus Minimax Playcited by 1
  16. 2026From No-Regret to Strategically Robust Learning in Repeated Auctionscited by 1
  17. 2022Online Learning in Supply-Chain Gamescited by 0
  18. 2025The Hidden Game Problemcited by 0
  19. 2025Learning Local Stackelberg Equilibria from Repeated Interactions with a Learning Agentcited by 0
  20. 2026Is Online Linear Optimization Sufficient for Strategic Robustness?cited by 0
  21. 2026Learning Safely Without Knowing the World:COMPASS-Hedgecited by 0