Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationality

TL;DR

This paper introduces an inverse game theory approach for Stackelberg games under bounded rationality, demonstrating that realistic behavioral models can improve the efficiency of inferring game parameters.

Contribution

It relaxes the assumption of perfect rationality to a bounded rationality model, showing that this leads to more efficient learning in inverse Stackelberg game settings.

Findings

Bounded rationality improves parameter inference efficiency.

Empirical results confirm theoretical advantages.

Robustness beyond the quantal response model.

Abstract

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem -- instead of prescribing equilibrium of a given game, we may directly observe the agents' equilibrium behaviors but want to infer the underlying parameters of an unknown game. This research question, also known as inverse game theory, has been studied in multiple recent works in the context of Stackelberg games. Unfortunately, existing works exhibit quite negative results, showing statistical hardness and computational hardness, assuming follower's perfectly rational behaviors. Our work relaxes the perfect rationality agent assumption to the classic quantal response model, a more realistic behavior model of bounded rationality. Interestingly, we show that the smooth property brought by such bounded rationality model actually leads to provably more efficient learning of the follower utility parameters in general Stackelberg games. Systematic empirical experiments on synthesized games confirm our theoretical results and further suggest its robustness beyond the strict quantal response model.