Complexity and Algorithms for Exploiting Quantal Opponents in Large Two-Player Games

Abstract

Solution concepts of traditional game theory assume entirely rational players; therefore, their ability to exploit subrational opponents is limited. One type of subrationality that describes human behavior well is the quantal response. While there exist algorithms for computing solutions against quantal opponents, they either do not scale or may provide strategies that are even worse than the entirely-rational Nash strategies. This paper aims to analyze and propose scalable algorithms for computing effective and robust strategies against a quantal opponent in normal-form and extensive-form games. Our contributions are: (1) we define two different solution concepts related to exploiting quantal opponents and analyze their properties; (2) we prove that computing these solutions is computationally hard; (3) therefore, we evaluate several heuristic approximations based on scalable counterfactual regret minimization (CFR); and (4) we identify a CFR variant that exploits the bounded opponents better than the previously used variants while being less exploitable by the worst-case perfectly-rational opponent.

Securing Lifelines: Safe Delivery of Critical Services in Areas with Volatile Security Situation via a Stackelberg Game Approach

“…Recent work explores the complexity of quantal response players in more generality for Stackelberg games (Cerny et al 2020;Milec et al 2021) calling the equilibrium as Quantal Stackelberg Equilbrium (QSE). Our problem differs because of an additional combinatorial dimension (operate a subset of centers) of the defender's action space.…”

Computing Quantal Stackelberg Equilibrium in Extensive-Form Games

“…The computed strategies did not correspond to a well-defined solution concept and were empirically suboptimal. We define and study this concept in our concurrent paper (Milec et al 2020). Besides rationality, in QSE, the leader also benefits from the power of commitment.…”