从玩家行为反推收益函数可能范围，给出最优估计精度。
Optimal Rates for Feasible Payoff Set Estimation in Games
- 基于观察到的策略行为，推断所有可能的收益函数集合。
- 在零和与非零和博弈中，首次实现豪斯多夫距离下最优学习速率。
- 适用于拍卖、定价等场景的反事实分析与机制设计。
研究两个玩家在双矩阵博弈中进行（近似）纳什均衡博弈，而学习者仅能观察其行动，对均衡或基础博弈无先验知识的情形。核心问题是：学习者能否通过观察行为反推玩家的收益函数？不同于单点估计，逆博弈论旨在识别与观察行为一致的所有收益函数集合，支持反事实分析与机制设计，如拍卖、定价与安全博弈等应用。本文聚焦于以高概率、ε精度（豪斯多夫度量）估计可行收益集的问题。我们首次给出了精确与近似均衡博弈下的极小极大最优率，涵盖零和与一般和博弈。结果为多智能体环境中集合值收益推断提供了学习理论基础。
原文摘要 · Abstract (English)
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is whether the learner can rationalize the observed behavior by inferring the players' payoff functions. Rather than producing a single payoff estimate, inverse game theory aims to identify the entire set of payoffs consistent with observed behavior, enabling downstream use in, e.g., counterfactual analysis and mechanism design across applications like auctions, pricing, and security games. We focus on the problem of estimating the set of feasible payoffs with high probability and up to precision $ε$ on the Hausdorff metric. We provide the first minimax-optimal rates for both exact and approximate equilibrium play, in zero-sum as well as general-sum games. Our results provide learning-theoretic foundations for set-valued payoff inference in multi-agent environments.
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