Selected work

Representative Papers

Evolutionarily Stable Stackelberg Equilibrium

Mar 18, 2026

This study addresses the challenge posed by mutant invasions to equilibrium stability in leader–follower games by proposing the evolutionarily stable Stackelberg equilibrium (SESS). In this framework, the leader commits to a mixed strategy while anticipating that a symmetric population of followers will adopt an evolutionarily stable strategy (ESS) in the subgame, subject to ecological constraints. This work is the first to explicitly incorporate evolutionary stability into the Stackelberg setting, distinguishing between the ESS choices of leaders and followers and thereby overcoming a key limitation of existing approaches that neglect resistance to mutations. Integrating game theory, ESS theory, and optimization algorithms, the authors develop an efficient computational method for SESS applicable to both discrete and continuous games, demonstrating its efficacy in biological contexts such as cancer therapy—where the physician acts as the leader and cancer cell phenotypes constitute the follower population.

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Computing Evolutionarily Stable Strategies in Multiplayer Games

Nov 25, 2025

This paper addresses the exact computation of all evolutionarily stable strategies (ESS) in nondegenerate normal-form games with three or more players. Overcoming the limitation of existing methods—restricted to two-player games—we propose the first general algorithmic framework for ESS identification. Leveraging the strict definition of ESS and the nondegeneracy assumption, we reformulate ESS verification as the joint solution of finitely many linear complementarity problems (LCPs). Our method performs a systematic enumeration of all possible pure-strategy support sets, coupled with symbolic feasibility verification, enabling complete and globally exhaustive ESS enumeration—without requiring initial guesses or convergence assumptions. Experiments across diverse classes of multiplayer games demonstrate the algorithm’s precision, computational efficacy, and robustness. To our knowledge, this is the first scalable, exact computational foundation for analyzing strategy stability in multi-agent systems.

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Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games

Sep 29, 2025

Computing exact Nash equilibria in multi-player imperfect-information games is computationally challenging, and existing algorithms—including Counterfactual Regret Minimization (CFR) and Fictitious Play—lack convergence guarantees. Method: This paper proposes a Quadratically Constrained Quadratic Programming (QCQP)-based approach formulated over the sequence-form representation of extensive-form games. It recasts equilibrium computation as a Nonlinear Complementarity Problem (NCP) and, for the first time, applies state-of-the-art nonconvex QCQP solvers. The method further integrates iterative dominance elimination to enhance computational efficiency. Results: Experiments on three-player Kuhn poker demonstrate that the algorithm rapidly computes exact Nash equilibria, significantly outperforming both Gambit (using enumeration and linear programming) and the Logit Quantal Response Equilibrium (QRE) method in both speed and accuracy. Moreover, it advances the equilibrium-computation paradigm beyond traditional normal-form game representations.

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Consistent Opponent Modeling of Static Opponents in Imperfect-Information Games

Aug 25, 2025

Existing opponent modeling approaches in imperfect-information games lack theoretical consistency and fail to guarantee asymptotic convergence to static opponent strategies. Method: We propose the first opponent modeling algorithm with formal consistency guarantees, formulated within the sequence-form representation of extensive-form games. Strategy inference is cast as a convex optimization problem, solved via projected gradient descent that jointly incorporates historical interaction data and real-time observations. Contribution: We provide a rigorous theoretical proof that the algorithm converges almost surely to the true opponent strategy as the number of interactions tends to infinity. Empirical evaluation across multiple imperfect-information games—including Leduc Hold’em and a simplified version of Dou Dizhu—demonstrates substantial improvements in long-term agent payoff. Moreover, the method exhibits robustness to observation noise and model misspecification, confirming its practical reliability under realistic conditions.

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Dominated Actions in Imperfect-Information Games

Apr 13, 2025

Solving for Nash equilibria in incomplete-information extensive-form games is hindered by exponential growth of the strategy space. Method: This paper formally defines “dominated actions” in extensive-form games and proposes a polynomial-time algorithm—combining linear programming with game-tree traversal—to rigorously identify both strictly and weakly dominated actions under mixed strategies. The method enables iterative pruning directly on the extensive-form representation, avoiding conversion to the exponentially larger normal-form representation. Crucially, it incorporates action-feasibility constraints (e.g., “All-In or Fold” in poker) to ensure correctness and practical applicability. Contribution/Results: The preprocessing step significantly reduces game size and accelerates equilibrium computation. Theoretically, the dominance detection is proven complete, with worst-case time complexity polynomial in the size of the game tree. Experimental results confirm substantial scalability improvements across benchmark games.

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Latest Papers

Evolutionarily Stable Stackelberg Equilibrium

Mar 18, 2026

This study addresses the challenge posed by mutant invasions to equilibrium stability in leader–follower games by proposing the evolutionarily stable Stackelberg equilibrium (SESS). In this framework, the leader commits to a mixed strategy while anticipating that a symmetric population of followers will adopt an evolutionarily stable strategy (ESS) in the subgame, subject to ecological constraints. This work is the first to explicitly incorporate evolutionary stability into the Stackelberg setting, distinguishing between the ESS choices of leaders and followers and thereby overcoming a key limitation of existing approaches that neglect resistance to mutations. Integrating game theory, ESS theory, and optimization algorithms, the authors develop an efficient computational method for SESS applicable to both discrete and continuous games, demonstrating its efficacy in biological contexts such as cancer therapy—where the physician acts as the leader and cancer cell phenotypes constitute the follower population.

0 citationsRead paper

Computing Evolutionarily Stable Strategies in Multiplayer Games

Nov 25, 2025

This paper addresses the exact computation of all evolutionarily stable strategies (ESS) in nondegenerate normal-form games with three or more players. Overcoming the limitation of existing methods—restricted to two-player games—we propose the first general algorithmic framework for ESS identification. Leveraging the strict definition of ESS and the nondegeneracy assumption, we reformulate ESS verification as the joint solution of finitely many linear complementarity problems (LCPs). Our method performs a systematic enumeration of all possible pure-strategy support sets, coupled with symbolic feasibility verification, enabling complete and globally exhaustive ESS enumeration—without requiring initial guesses or convergence assumptions. Experiments across diverse classes of multiplayer games demonstrate the algorithm’s precision, computational efficacy, and robustness. To our knowledge, this is the first scalable, exact computational foundation for analyzing strategy stability in multi-agent systems.

0 citationsRead paper

Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games

Sep 29, 2025

Computing exact Nash equilibria in multi-player imperfect-information games is computationally challenging, and existing algorithms—including Counterfactual Regret Minimization (CFR) and Fictitious Play—lack convergence guarantees. Method: This paper proposes a Quadratically Constrained Quadratic Programming (QCQP)-based approach formulated over the sequence-form representation of extensive-form games. It recasts equilibrium computation as a Nonlinear Complementarity Problem (NCP) and, for the first time, applies state-of-the-art nonconvex QCQP solvers. The method further integrates iterative dominance elimination to enhance computational efficiency. Results: Experiments on three-player Kuhn poker demonstrate that the algorithm rapidly computes exact Nash equilibria, significantly outperforming both Gambit (using enumeration and linear programming) and the Logit Quantal Response Equilibrium (QRE) method in both speed and accuracy. Moreover, it advances the equilibrium-computation paradigm beyond traditional normal-form game representations.

0 citationsRead paper

Consistent Opponent Modeling of Static Opponents in Imperfect-Information Games

Aug 25, 2025

Existing opponent modeling approaches in imperfect-information games lack theoretical consistency and fail to guarantee asymptotic convergence to static opponent strategies. Method: We propose the first opponent modeling algorithm with formal consistency guarantees, formulated within the sequence-form representation of extensive-form games. Strategy inference is cast as a convex optimization problem, solved via projected gradient descent that jointly incorporates historical interaction data and real-time observations. Contribution: We provide a rigorous theoretical proof that the algorithm converges almost surely to the true opponent strategy as the number of interactions tends to infinity. Empirical evaluation across multiple imperfect-information games—including Leduc Hold’em and a simplified version of Dou Dizhu—demonstrates substantial improvements in long-term agent payoff. Moreover, the method exhibits robustness to observation noise and model misspecification, confirming its practical reliability under realistic conditions.

0 citationsRead paper

Dominated Actions in Imperfect-Information Games

Apr 13, 2025

Solving for Nash equilibria in incomplete-information extensive-form games is hindered by exponential growth of the strategy space. Method: This paper formally defines “dominated actions” in extensive-form games and proposes a polynomial-time algorithm—combining linear programming with game-tree traversal—to rigorously identify both strictly and weakly dominated actions under mixed strategies. The method enables iterative pruning directly on the extensive-form representation, avoiding conversion to the exponentially larger normal-form representation. Crucially, it incorporates action-feasibility constraints (e.g., “All-In or Fold” in poker) to ensure correctness and practical applicability. Contribution/Results: The preprocessing step significantly reduces game size and accelerates equilibrium computation. Theoretically, the dominance detection is proven complete, with worst-case time complexity polynomial in the size of the game tree. Experimental results confirm substantial scalability improvements across benchmark games.

0 citationsRead paper