Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents
This addresses strategic interactions in real-life applications like security and classification by modeling agents with calibrated forecasts, offering a more robust framework than standard assumptions.
The paper tackles the problem of Stackelberg games where agents use calibrated forecasts instead of direct access to the principal's actions, introducing Calibrated Stackelberg Games (CSGs) and adaptive calibration. It shows that the principal's utility converges to the optimal Stackelberg value in both finite and continuous settings, with applications in security games and strategic classification.
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.