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Games
Special Issues
New Advances in Computational Game Theory and Its Applications
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New Advances in Computational Game Theory and Its Applications

A Special Issue of Games (ISSN 2073-4336) belonging to the section "Algorithmic and Computational Game Theory".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 2274

Editor

Dr. Sam Ganzfried

E-Mail Website
Guest Editor
1. Ganzfried Research, Miami Beach, FL 33139, USA
2. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA
Interests: artificial intelligence; game theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many fundamental problems in game theory are computationally challenging; for example, computing one Nash equilibrium in two-player general-sum normal-form games is PPAD-complete, and it is widely believed that no efficient (polynomial-time) algorithms exist. The problem only becomes harder as additional elements of complexity are introduced, including: more than two players, stochastic events, imperfect information, very large strategy spaces, repeated interactions, learning to exploit weaknesses of suboptimal opponents, and new solution concepts. In order to create strong agents for complex multiagent real-world interactions, it is essential to develop effective scalable methods that address these computational challenges.

Dr. Sam Ganzfried
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Games is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Nash equilibrium computation and approximation
  • computation of equilibrium refinements
  • alternative solution concepts and their computation
  • learning in games
  • stochastic games
  • imperfect information
  • applications including security, biology, education, law, and political science

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Published Papers (2 papers)

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Research

21 pages, 1022 KB  
Article
An Extreme Learning Machine-Based Method for Solving Linear–Quadratic Nonzero-Sum Differential Games
by Changdong Duan and Yuefei Yuan
Games 2026, 17(4), 42; https://doi.org/10.3390/g17040042 - 6 Aug 2026
Viewed by 230
Abstract
Multi-agent interaction in linear–quadratic (LQ) differential games gives rise to open-loop Nash equilibria that rarely admit closed-form expressions, motivating the development of reliable numerical solvers. Classical approaches such as shooting and spectral collocation are sensitive to the initial guess on the unknown boundary [...] Read more.
Multi-agent interaction in linear–quadratic (LQ) differential games gives rise to open-loop Nash equilibria that rarely admit closed-form expressions, motivating the development of reliable numerical solvers. Classical approaches such as shooting and spectral collocation are sensitive to the initial guess on the unknown boundary values and accumulate discretisation error over long horizons, while deep-learning alternatives require iterative gradient-based training with architecture- and convergence-specific overhead. To overcome these limitations, we recast the LQ nonzero-sum game as a linear two-point boundary value problem (TPBVP) via the Pontryagin maximum principle (PMP) and solve it with a single-layer feedforward neural network (SLFN) in which hidden-layer parameters are sampled once and fixed. The state and all player-specific costates are parameterised by random hidden features on a uniform time grid, the boundary conditions are appended as dedicated rows of the linear collocation system, and the output weights follow from a single Moore–Penrose pseudoinverse, entirely bypassing gradient-based iteration. For the scalar LQ optimal-control TPBVP, a residual-to-solution stability theorem converts the continuous equation and boundary residuals into uniform state, costate, control, and cost error bounds. Validation across two-player low- and high-dimensional benchmarks, a heterogeneous three-player game, and paired seed sweeps confirms high accuracy against analytical and matrix-exponential references, while revealing that no single activation function dominates across all problem types: tanh is most accurate in one-dimensional settings, and Gaussian RBF leads in multidimensional cases. Full article
(This article belongs to the Special Issue New Advances in Computational Game Theory and Its Applications)
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12 pages, 249 KB  
Article
Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games
by Sam Ganzfried
Games 2026, 17(1), 9; https://doi.org/10.3390/g17010009 - 3 Feb 2026
Viewed by 1181
Abstract
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer normal-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have [...] Read more.
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer normal-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. We present an approach for exact computation of Nash equilibrium in multiplayer imperfect-information games that solves a quadratically-constrained program based on a nonlinear complementarity problem formulation from the sequence-form game representation. This approach capitalizes on recent advances for solving nonconvex quadratic programs. Our algorithm is able to quickly solve three-player Kuhn poker after removal of dominated actions. Of the available algorithms in the Gambit software suite, only the logit quantal response approach is successfully able to solve the game; however, the approach takes longer than our algorithm and also involves a degree of approximation. Our formulation also leads to a new approach for computing Nash equilibrium in multiplayer normal-form games which we demonstrate to outperform a previous quadratically-constrained program formulation. Full article
(This article belongs to the Special Issue New Advances in Computational Game Theory and Its Applications)
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