In this paper, we introduce a generalization of the standard Stackelberg Games (SGs) framework: Calibrated Stackelberg Games (CSGs). In CSGs, a principal repeatedly interacts with an agent who (contrary to standard SGs) does not have direct access to the principal's action but instead best-responds to calibrated forecasts about it. CSG is a powerful modeling tool that goes beyond assuming that agents use ad hoc and highly specified algorithms for interacting in strategic settings and thus more robustly addresses real-life applications that SGs were originally intended to capture. Along with CSGs, we also introduce a stronger notion of calibration, termed adaptive calibration, that provides fine-grained any-time calibration guarantees against adversarial sequences. We give a general approach for obtaining adaptive calibration algorithms and specialize them for finite CSGs. In our main technical result, we show that in CSGs, the principal can achieve utility that converges to the optimum Stackelberg value of the game both in finite and continuous settings, and that no higher utility is achievable. Two prominent and immediate applications of our results are the settings of learning in Stackelberg Security Games and strategic classification, both against calibrated agents.

本文介绍了一种扩展标准 Stackelberg Games 框架的模型：Calibrated Stackelberg Games(CSGs)，同时引入了更强的校准概念——自适应校准，给出了一般性方法来获得自适应校准算法，并将其应用于诸如 Stackelberg 安全博弈和战略分类等领域中。

校准的斯塔克伯格博弈: 对抗校准智能体的最优化承诺学习