Tootfinder

Nash equilibria in semidefinite games and Lemke-Howson paths
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas, Antonios Varvitsiotis
https://arxiv.org/abs/2506.11940

Nash equilibria in semidefinite games and Lemke-Howson paths
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the computation of Nash equilibria in such games as semidefinite complementarity problems and develop symbolic-numeric techniques to trace generalized Lemke-Howson paths. These paths generalize the piecewise affine-linear trajectories of the classical Lemke-Howson algorithm for bimatrix games, replacing them with nonline…

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
Jiarui Gan, Rupak Majumdar
https://arxiv.org/abs/2506.07186

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this poses new representational and algorithmic challenges as the number of possible histories grows exponentially with the number of time steps. We focus on computing $(ε, δ)$-optimal CEs -- solutions that achieve a value within $ε$ of an optimal CE, while al…

This https://arxiv.org/abs/2505.24171 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

A note on the diversity Owen values
Béal et al. (Int J Game Theory 54, 2025) introduce the Diversity Owen value for TU-games with diversity constraints, and provide axiomatic characterizations using the axioms of fairness and balanced contributions. However, there exist logical flaws in the proofs of the uniqueness of these characterizations. In this note we provides the corrected proofs of the characterizations by introducing the null player for diversity games axiom. Also, we establish two alternative characterizations of the …

This https://arxiv.org/abs/2505.20011 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

The Many Challenges of Human-Like Agents in Virtual Game Environments
Human-like agents are an increasingly important topic in games and beyond. Believable non-player characters enhance the gaming experience by improving immersion and providing entertainment. They also offer players the opportunity to engage with AI entities that can function as opponents, teachers, or cooperating partners. Additionally, in games where bots are prohibited -- and even more so in non-game environments -- there is a need for methods capable of identifying whether digital interaction…

This https://arxiv.org/abs/2404.15483 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strategy Complexity of Büchi Objectives in Concurrent Stochastic Games
We study 2-player zero-sum concurrent (i.e., simultaneous move) stochastic Büchi games and Transience games on countable graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of satisfying the game objective. The Büchi objective is to visit a given set of target states infinitely often. This can be seen as a special case of maximizing the expected $\limsup$ of the daily rewards, where all daily rewards are in $\{0,1\}$. The Transience objective is to vis…

The Complexity of Correlated Equilibria in Generalized Games
Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Gabriele Farina
https://arxiv.org/abs/2506.01899

The Complexity of Correlated Equilibria in Generalized Games
Correlated equilibria -- and their generalization $Φ$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model funda…

A note on the diversity Owen values
Songtao He, Erfang Shan, Xinyu Sun
https://arxiv.org/abs/2505.24171 https://arxiv.org/pdf/2505.24…

A note on the diversity Owen values
Béal et al. (Int J Game Theory 54, 2025) introduce the Diversity Owen value for TU-games with diversity constraints, and provide axiomatic characterizations using the axioms of fairness and balanced contributions. However, there exist logical flaws in the proofs of the uniqueness of these characterizations. In this note we provides the corrected proofs of the characterizations by introducing the null player for diversity games axiom. Also, we establish two alternative characterizations of the …

This https://arxiv.org/abs/2506.02520 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Branch-and-Cut for Mixed-Integer Generalized Nash Equilibrium Problems
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player depends on the strategies chosen by the rival players. In this work, we introduce a branch-and-cut algorithm to compute exact pure Nash equilibria for different classes of such mixed-integer games. The main idea is to reformulate the equilibrium problem as a sui…

Branch-and-Cut for Mixed-Integer Generalized Nash Equilibrium Problems
Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz
https://arxiv.org/abs/2506.02520

Branch-and-Cut for Mixed-Integer Generalized Nash Equilibrium Problems
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player depends on the strategies chosen by the rival players. In this work, we introduce a branch-and-cut algorithm to compute exact pure Nash equilibria for different classes of such mixed-integer games. The main idea is to reformulate the equilibrium problem as a sui…

This https://arxiv.org/abs/2403.07932 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Feint Behaviors and Strategies: Formalization, Implementation and Evaluation
Feint behaviors refer to a set of deceptive behaviors in a nuanced manner, which enable players to obtain temporal and spatial advantages over opponents in competitive games. Such behaviors are crucial tactics in most competitive multi-player games (e.g., boxing, fencing, basketball, motor racing, etc.). However, existing literature does not provide a comprehensive (and/or concrete) formalization for Feint behaviors, and their implications on game strategies. In this work, we introduce the firs…

This https://arxiv.org/abs/2502.20770 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Learning to Steer Learners in Games
We consider the problem of learning to exploit learning algorithms through repeated interactions in games. Specifically, we focus on the case of repeated two player, finite-action games, in which an optimizer aims to steer a no-regret learner to a Stackelberg equilibrium without knowledge of its payoffs. We first show that this is impossible if the optimizer only knows that the learner is using an algorithm from the general class of no-regret algorithms. This suggests that the optimizer require…

Polynomial Expectation Property for Max-Polymatrix Games
Howard Dai
https://arxiv.org/abs/2506.01343 https://arxiv.org/pdf/2506.01343…

Polynomial Expectation Property for Max-Polymatrix Games
We address an open question which addresses the computability of correlated equilibria in a variant of polymatrix where each player's utility is the maximum of their edge payoffs. We demonstrate that this max-variant game has the polynomial expectation property, and conclude that there indeed exists a polynomial correlated equilibrium scheme.

This https://arxiv.org/abs/2502.20466 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Semicoarse Correlated Equilibria and LP-Based Guarantees for Gradient Dynamics in Normal-Form Games
Projected gradient ascent is known to satisfy no-external regret as a learning algorithm. However, recent empirical work shows that projected gradient ascent often finds the Nash equilibrium in settings beyond two-player zero-sum interactions or potential games, including those where the set of coarse correlated equilibria is very large. We show that gradient ascent in fact satisfies a stronger class of linear $Φ$-regret in normal-form games; resulting in a refined solution concept which we du…

This https://arxiv.org/abs/2505.14547 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

GUARD: Constructing Realistic Two-Player Matrix and Security Games for Benchmarking Game-Theoretic Algorithms
Game-theoretic algorithms are commonly benchmarked on recreational games, classical constructs from economic theory such as congestion and dispersion games, or entirely random game instances. While the past two decades have seen the rise of security games -- grounded in real-world scenarios like patrolling and infrastructure protection -- their practical evaluation has been hindered by limited access to the datasets used to generate them. In particular, although the structural components of the…

Online Competitive Information Gathering for Partially Observable Trajectory Games
Mel Krusniak, Hang Xu, Parker Palermo, Forrest Laine
https://arxiv.org/abs/2506.01927

Online Competitive Information Gathering for Partially Observable Trajectory Games
Game-theoretic agents must make plans that optimally gather information about their opponents. These problems are modeled by partially observable stochastic games (POSGs), but planning in fully continuous POSGs is intractable without heavy offline computation or assumptions on the order of belief maintained by each player. We formulate a finite history/horizon refinement of POSGs which admits competitive information gathering behavior in trajectory space, and through a series of approximations,…