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Mathematics
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AI in Game Theory: Theory and Applications
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AI in Game Theory: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 4051

Special Issue Editors

Dr. Alessia Donato

E-Mail Website
Guest Editor
Department of Engineering, University of Messina, 98100 Messina, Italy
Interests: Game Theory; multi-objective optimization; evolutionary algorithms; patent analysis; environmental sustainability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. David Carfì

E-Mail Website
Guest Editor
1. Department of Mathematics, University of California, Riverside, CA 92521, USA
2. Department of Economics, University of Messina, 98122 Messina, Italy
Interests: mathematical economics; Game Theory; decision theory; risk management; bargaining theory; finance; econophysics; quantum finance; quantum mechanics; schwartz distribution theory; differential manifolds; relativity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

In Game Theory, every agent tries to maximize their own profit (utility, payoff, …), in possible competition (mutual dependence) with each other, and, therefore, optimal decisions occur in the presence of utility tradeoffs.

In comparison to a simple multi-objective optimization problem, in Game Theory, the payoff functions of the players vary, showing an interdependence, a kind of indirect interaction, since the payoff of one player depends also upon the strategies of the other players; any player directly affects the payoffs of the others. Often, when binding agreements are allowed, the complex nature of the interaction does not allow us to find compromised solutions in closed-forms. In this case, solving the problem consists of computing (or approximating) a representative boundary of Pareto optimal solutions.

Evolutionary algorithms, which are evolutionary AI-based computer applications, are popular approaches that generate Pareto optimal solutions to Game Theory problems. They use mechanisms that are typically associated with biological evolution and solve problems by continuously exploring promising search space.

AI can so improve decision-making in Game Theory thanks to the ability of rapidly analyzing big sets of data while simulating many different scenarios of the strategy spaces, and thanks to the ability of remembering what happened in previous games and taking into account the most convenient search space for improving the solution.

In this Special Issue, we encourage submissions providing possible applications of AI in Game Theory. The topics of interest for this publication include, but are not limited to, the following:

  • Artificial Intelligence in Game Theory.
  • Artificial Intelligence in decision-making.
  • Evolutionary algorithms in Game Theory.

Machine learning in Pareto fronts.

Dr. Alessia Donato
Prof. Dr. David Carfì
Guest Editors

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 single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics 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 2600 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

  • artificial intelligence
  • Game Theory
  • decision-making
  • evolutionary algorithm
  • Pareto front
  • machine learning

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Published Papers (3 papers)

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26 pages, 961 KB  
Article
Statistical Privacy-Preserving Distributed Online Aggregative Games via Mirror Descent with Correlated Perturbations
by Meng Yuan and Rui Yu
Mathematics 2026, 14(10), 1731; https://doi.org/10.3390/math14101731 - 18 May 2026
Abstract
Distributed online aggregative games are widely used to model sequential decision-making problems in dynamic networked systems. However, the repeated information exchange required by distributed algorithms may disclose players’ sensitive local data. This paper investigates a privacy-preserving distributed online aggregative game over multi-agent networks. [...] Read more.
Distributed online aggregative games are widely used to model sequential decision-making problems in dynamic networked systems. However, the repeated information exchange required by distributed algorithms may disclose players’ sensitive local data. This paper investigates a privacy-preserving distributed online aggregative game over multi-agent networks. A distributed online mirror descent algorithm with correlated perturbations is developed to protect local private information. Under standard assumptions, an expected dynamic regret bound and a statistical privacy guarantee are established for the proposed algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm and reveal the tradeoff between privacy protection and algorithmic performance. Full article
(This article belongs to the Special Issue AI in Game Theory: Theory and Applications)
36 pages, 997 KB  
Article
Genetic Algorithms for Pareto Optimization in Bayesian Cournot Games Under Incomplete Cost Information
by David Carfí, Alessia Donato and Emanuele Perrone
Mathematics 2026, 14(5), 762; https://doi.org/10.3390/math14050762 - 25 Feb 2026
Viewed by 523
Abstract
This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval [c*, c*] with [...] Read more.
This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval [c*, c*] with 0<c*<c*<∞. The infinite dimensionality of the functional strategy spaces (mappings from types to production quantities) renders analytical closed-form solutions infeasible in this continuous-type setting. To overcome this challenge, we restrict the strategy spaces to finite-dimensional differentiable sub-manifolds—specifically, one-parameter families of oscillatory functions (cosine, sine, and mixed forms). After suitable affine Q-rescaling to map the oscillatory range into the production interval [0, Q], and with parameter ranges satisfying α, β>(π/2)/c*, these curves ensure near-exhaustivity: the joint production map (α, β)↦(xα(s), yβ(t)) covers [0, Q]2 densely for every fixed cost pair (s, t), thereby recovering (up to density and closure) the full ex-post payoff space. We introduce the ex-post payoff mapping Φ(s, t, x, y)=(es(x, y)(t), ft(x, y)(s)), which collects every realizable payoff pair once nature draws the types and players select their strategies. The image of Φ defines the general payoff space of the game, and its non-dominated points constitute the general ex-post Pareto frontier—all efficient realized outcomes across type-strategy realizations, without dependence on private probability measures over types. Using multi-objective genetic algorithms, we numerically approximate this frontier (and selected collusive compromises) within the restricted but representative sub-manifolds. The resulting frontiers are computationally accessible, robust to parameter variations, and validated through hypervolume convergence, sensitivity analysis, and comparisons with NSGA-II, PSO and scalarization methods. The findings are significant because they provide decision-makers in oligopolistic markets (e.g., electric vehicles) with viable, implementable production policies that explore efficient trade-offs under genuine cost uncertainty, without requiring explicit forecasts of the opponent’s type distribution—a limitation of traditional expected-utility approaches. By focusing on ex-post efficiency, the method reveals belief-independent compromise solutions that may guide tacit coordination or collusive outcomes in real-world strategic settings. Full article
(This article belongs to the Special Issue AI in Game Theory: Theory and Applications)
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23 pages, 830 KB  
Article
A Novel Multi-Task Learning Framework for Interval-Valued Carbon Price Forecasting Using Online News and Search Engine Data
by Dinggao Liu, Liuqing Wang, Shuo Lin and Zhenpeng Tang
Mathematics 2025, 13(3), 455; https://doi.org/10.3390/math13030455 - 29 Jan 2025
Cited by 6 | Viewed by 2558
Abstract
The European Union Emissions Trading System (EU ETS) serves as the cornerstone of European climate policy, providing a critical mechanism for mitigating greenhouse gas emissions. Accurate forecasting of the carbon allowance prices within the market is essential for policymakers, enterprises, and investors. To [...] Read more.
The European Union Emissions Trading System (EU ETS) serves as the cornerstone of European climate policy, providing a critical mechanism for mitigating greenhouse gas emissions. Accurate forecasting of the carbon allowance prices within the market is essential for policymakers, enterprises, and investors. To address the need for interval-valued time series modeling and forecasting in the carbon market, this paper proposes a Transformer-based multi-task learning framework that integrates online news and search engine data information to forecast interval-valued EU carbon allowance futures prices. Empirical evaluations demonstrate that the proposed framework achieves superior predictive accuracy for short-term forecasting and remains robust under high market volatility and economic policy uncertainty compared to single-task learning benchmarks. Furthermore, ablation experiments indicate that incorporating news sentiment intensity and search index effectively enhances the framework’s predictive performance. Interpretability analysis highlights the critical role of specific temporal factors, while the time-varying variable importance analysis further underscores the influence of carbon allowance close prices and key energy market variables and also recognizes the contributions of news sentiment. In summary, this study provides valuable insights for policy management, risk hedging, and portfolio decision-making related to interval-valued EU carbon prices and offers a robust forecasting tool for carbon market prediction. Full article
(This article belongs to the Special Issue AI in Game Theory: Theory and Applications)
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