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

Milec, David; Černý, Jakub; Lisý, Viliam; An, Bo

doi:10.48550/arxiv.2009.14521

Cited by 2 publications

(1 citation statement)

References 30 publications

(17 reference statements)

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“…Network security games and others. Our work also relates to static Stackelberg security game models with Quantal Response adversaries [Černỳ et al, 2021, Haghtalab et al, 2016, Mai and Sinha, 2022, Milec et al, 2020, Yang et al, 2011, 2012. In dynamic models named as network security games [Jain et al, 2011], the set-up is different from our work as in this work the rational adversary aims to reach a target and stop, whereas in our work the boundedly rational adversary can attack multiple targets.…”

Section: Related Workmentioning

confidence: 99%

Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary

Mai¹,

Avinandan²,

Sinha³

et al. 2023

Preprint

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This work studies Stackelberg network interdiction games -an important class of games in which a defender first allocates (randomized) defense resources to a set of critical nodes on a graph while an adversary chooses its path to attack these nodes accordingly. We consider a boundedly rational adversary in which the adversary's response model is based on a dynamic form of classic logit-based discrete choice models. We show that the problem of finding an optimal interdiction strategy for the defender in the rational setting is NP-hard. The resulting optimization is in fact non-convex and additionally, involves complex terms that sum over exponentially many paths. We tackle these computational challenges by presenting new efficient approximation algorithms with bounded solution guarantees. First, we address the exponentially-many-path challenge by proposing a polynomial-time dynamic programming-based formulation. We then show that the gradient of the non-convex objective can also be computed in polynomial time, which allows us to use a gradient-based method to solve the problem efficiently. Second, we identify a restricted problem that is convex and hence gradient-based methods find the global optimal solution for this restricted problem. We further identify mild conditions under which this restricted problem provides a bounded approximation for the original problem.

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Section: Related Workmentioning

confidence: 99%

Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary

Mai¹,

Avinandan²,

Sinha³

et al. 2023

Preprint

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Computing Quantal Stackelberg Equilibrium in Extensive-Form Games

Černý

Lisý

Bošanský

et al. 2021

AAAI

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Deployments of game-theoretic solution concepts in the real world have highlighted the necessity to consider human opponents' boundedly rational behavior. If subrationality is not addressed, the system can face significant losses in terms of expected utility. While there exist algorithms for computing optimal strategies to commit to when facing subrational decision-makers in one-shot interactions, these algorithms cannot be generalized for solving sequential scenarios because of the inherent curse of strategy-space dimensionality in sequential games and because humans act subrationally in each decision point separately. We study optimal strategies to commit to against subrational opponents in sequential games for the first time and make the following key contributions: (1) we prove the problem is NP-hard in general; (2) to enable further analysis, we introduce a non-fractional reformulation of the direct non-concave representation of the equilibrium; (3) we identify conditions under which the problem can be approximated in polynomial time in the size of the representation; (4) we show how an MILP can approximate the reformulation with a guaranteed bounded error, and (5) we experimentally demonstrate that our algorithm provides higher quality results several orders of magnitude faster than a baseline method for general non-linear optimization.

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

Cited by 2 publications

References 30 publications

Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary

Tackling Stackelberg Network Interdiction against a Boundedly Rational Adversary

Computing Quantal Stackelberg Equilibrium in Extensive-Form Games

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