Author name cluster

Jakub Černý

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

9 papers

1 author row

AAAI Conference 2026 Conference Paper

Colonel Blotto with Battlefield Games

Salam Afiouni
Jakub Černý
Chun Kai Ling
Christian Kroer

We study a class of two-player zero-sum Colonel Blotto games in which, after allocating soldiers across battlefields, players engage in (possibly distinct) normal-form games on each battlefield. Per-battlefield payoffs are parameterized by the soldier allocations. This generalizes the classical Blotto setting, where outcomes depend only on relative soldier allocations. We consider both discrete and continuous allocation models and examine two types of aggregate objectives: linear aggregation and worst-case battlefield value. For each setting, we analyze the existence and computability of Nash equilibrium. The general problem is not convex-concave, which limits the applicability of standard convex optimization techniques. However, we show that in several settings it is possible to reformulate the strategy space in a way where convex-concave structure is recovered. We evaluate the proposed methods on synthetic and real-world instances inspired by security applications, suggesting that our approaches scale well in practice.

PDF Details DOI

AAAI Conference 2026 Conference Paper

Security Games with Layered Defenses: Adaptive Adversaries and Gittins Indices

Chun Kai Ling
Jakub Černý
Chin Hui Han
Garud Iyengar
Christian Kroer

Real-world security applications (e.g., cybersecurity) often involve multiple attack paths, each with layers of defenses that an attacker needs to sequentially overcome before a successful attack on the entire system. Each defensive resource changes dynamically in efficacy as the attack unfolds. In this paper, we study the case where attackers are adaptive, potentially switching paths over time in response to these changes with the goal to minimize the expected time until a successful attack. We formalize this as a min-max game and give examples where adaptive attackers are more powerful than non-adaptive ones. We show that defenses that do not account for adaptivity can perform arbitrarily worse. A connection between the attacker's optimal strategy with the classical theory of multi-armed bandits and the Gittins index is made, yielding a simple gradient based algorithm to solve our proposed min-max game. Experiments on synthetic settings validate our approach.

PDF Details DOI

AAAI Conference 2026 Conference Paper

Spatial Branch-and-Bound for Computing Multiplayer Nash Equilibrium

Jakub Černý
Shuvomoy Das Gupta
Christian Kroer

Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in elections or assess policy impacts in integrated assessment models. However, efficiently computing these equilibria requires games to have a carefully designed structure and satisfy numerous restrictions; otherwise, the computational complexity becomes prohibitive. In particular, finding even approximate Nash equilibria in general normal-form games with three or more players is known to be PPAD-complete. Current state-of-the-art algorithms for computing Nash equilibria in multiplayer normal-form games either suffer from poor scalability due to their reliance on non-convex optimization solvers, or lack guarantees of convergence to a true equilibrium. In this paper, we propose a novel reformulation of the Nash equilibrium computation problem and develop a complete and sound spatial branch-and-bound algorithm based on this reformulation. We provide a qualitative analysis arguing why one should expect our approach to perform better than conventional formulation, and show the relationship between approximate solution to our reformulation and that of computing an approximate Nash equilibrium. Empirical evaluations demonstrate that our algorithm substantially outperforms existing complete methods.

PDF Details DOI

AAAI Conference 2025 Conference Paper

Commitment to Sparse Strategies in Two-Player Games

Salam Afiouni
Jakub Černý
Chun Kai Ling
Christian Kroer

While Nash equilibria are guaranteed to exist, they may exhibit dense support, making them difficult to understand and execute in some applications. In this paper, we study k-sparse commitments in games where one player is restricted to mixed strategies with support size at most k. Finding k-sparse commitments is known to be computationally hard. We start by showing several structural properties of k-sparse solutions, including that the optimal support may vary dramatically as k increases. These results suggest that naive greedy or double-oracle-based approaches are unlikely to yield practical algorithms. We then develop a simple approach based on mixed integer linear programs (MILPs) for zero-sum games, general-sum Stackelberg games, and various forms of structured sparsity. We also propose practical algorithms for cases where one or both players have large (i.e., practically innumerable) action sets, utilizing a combination of MILPs and incremental strategy generation. We evaluate our methods on synthetic and real-world scenarios based on security applications. In both settings, we observe that even for small support sizes, we can obtain more than 90% of the true Nash value while maintaining a reasonable runtime, demonstrating the significance of our formulation and algorithms.

PDF Details DOI

AAMAS Conference 2023 Conference Paper

Price of Anarchy in a Double-Sided Critical Distribution System

David Sychrovský
Jakub Černý
Sylvain Lichau
Martin Loebl

Measures of allocation optimality differ significantly when distributing standard tradable goods in peaceful times and scarce resources in crises. While realistic markets offer asymptotic efficiency, they may not necessarily guarantee fair allocation desirable when distributing the critical resources. To achieve fairness, mechanisms often rely on a central authority, which may act inefficiently in times of need when swiftness and good organization are crucial. In this work, we study a hybrid trading system called Crisdis, introduced by Jedličková et al. , which combines fair allocation of buying rights with a market – leveraging the best of both worlds. A frustration of a buyer in Crisdis is defined as a difference between the amount of goods they are entitled to according to the assigned buying rights and the amount of goods they are able to acquire by trading. We define a Price of Anarchy (PoA) in this system as a conceptual analogue of the original definition in the context of frustration. Our main contribution is a study of PoA in realistic complex double-sided market mechanisms for Crisdis. The performed empirical analysis suggests that in contrast to market free of governmental interventions, the PoA in our system decreases.

PDF

AAAI Conference 2023 Conference Paper

Solving Large-Scale Pursuit-Evasion Games Using Pre-trained Strategies

Shuxin Li
Xinrun Wang
Youzhi Zhang
Wanqi Xue
Jakub Černý
Bo An

Pursuit-evasion games on graphs model the coordination of police forces chasing a fleeing felon in real-world urban settings, using the standard framework of imperfect-information extensive-form games (EFGs). In recent years, solving EFGs has been largely dominated by the Policy-Space Response Oracle (PSRO) methods due to their modularity, scalability, and favorable convergence properties. However, even these methods quickly reach their limits when facing large combinatorial strategy spaces of the pursuit-evasion games. To improve their efficiency, we integrate the pre-training and fine-tuning paradigm into the core module of PSRO -- the repeated computation of the best response. First, we pre-train the pursuer's policy base model against many different strategies of the evader. Then we proceed with the PSRO loop and fine-tune the pre-trained policy to attain the pursuer's best responses. The empirical evaluation shows that our approach significantly outperforms the baselines in terms of speed and scalability, and can solve even games on street maps of megalopolises with tens of thousands of crossroads -- a scale beyond the effective reach of previous methods.

PDF Details DOI

AAAI Conference 2021 Conference Paper

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

David Milec
Jakub Černý
Viliam Lisý
Bo An

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.

PDF Details

AAAI Conference 2021 Conference Paper

Computing Ex Ante Coordinated Team-Maxmin Equilibria in Zero-Sum Multiplayer Extensive-Form Games

Youzhi Zhang
Bo An
Jakub Černý

Computational game theory has many applications in the modern world in both adversarial situations and the optimization of social good. While there exist many algorithms for computing solutions in two-player interactions, finding optimal strategies in multiplayer interactions efficiently remains an open challenge. This paper focuses on computing the multiplayer Team-Maxmin Equilibrium with Coordination device (TMECor) in zero-sum extensive-form games. TMECor models scenarios when a team of players coordinates ex ante against an adversary. Such situations can be found in card games (e. g. , in Bridge and Poker), when a team works together to beat a target player but communication is prohibited; and also in real world, e. g. , in forest-protection operations, when coordinated groups have limited contact during interdicting illegal loggers. The existing algorithms struggle to find a TMECor efficiently because of their high computational costs. To compute a TMECor in larger games, we make the following key contributions: (1) we propose a hybrid-form strategy representation for the team, which preserves the set of equilibria; (2) we introduce a column-generation algorithm with a guaranteed finite-time convergence in the infinite strategy space based on a novel best-response oracle; (3) we develop an associated-representation technique for the exact representation of the multilinear terms in the best-response oracle; and (4) we experimentally show that our algorithm is several orders of magnitude faster than prior state-of-the-art algorithms in large games.

PDF Details

AAAI Conference 2021 Conference Paper

Computing Quantal Stackelberg Equilibrium in Extensive-Form Games

Jakub Černý
Viliam Lisý
Branislav Bošanský
Bo An

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.

PDF Details