Modern Trends in Game Theory and Optimal Control

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 310

Special Issue Editors


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Guest Editor
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong 999077, China
Interests: stochastic and mean field games; stochastic control theory; optimal trading in illiquid markets; optimal investment and consumption problems

E-Mail Website
Guest Editor
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong 999077, China
Interests: mathematical finance; financial engineering; behavioral finance; insurance; risk management; stochastic control; free boundary problem in finance

Special Issue Information

Dear Colleagues,

This Special Issue on “Modern Trends in Game Theory and Optimal Control” will focus on the latest advancements in the methodologies and applications of game theory and optimal control, including, but not limited to, mean field games and mean field control. We seek articles that compare existing frameworks with emerging approaches, as well as those that provide an overview of new models and numerical analyses. Contributions are expected to encompass either general theoretical developments or specific applications across various fields, including, but not limited to, financial mathematics, engineering, and machine learning.

We encourage submissions that avoid purely conjectural approaches. We welcome authors from around the globe, particularly those engaged in rigorous research that advances our understanding of game theory and optimal control in contemporary settings.

Dr. Guanxing Fu
Dr. Zuoquan Xu
Guest Editors

Manuscript Submission Information

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Keywords

  • stochastic control
  • game theory
  • mean field game
  • mean field control
  • financial mathematics

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Published Papers (1 paper)

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Research

19 pages, 734 KiB  
Article
Emission Control in an n-Firm Oligopoly Game with Product Differentiation
by Akio Matsumoto and Ferenc Szidarovszky
Mathematics 2025, 13(12), 2007; https://doi.org/10.3390/math13122007 - 18 Jun 2025
Viewed by 126
Abstract
Is it possible to control NPS (non-point source) pollution whose sources, sizes, and origins are difficult to identify? This study provides a positive answer in a non-cooperative n-firm oligopoly model in which the firms determine levels of differentiated goods and abatement technologies. [...] Read more.
Is it possible to control NPS (non-point source) pollution whose sources, sizes, and origins are difficult to identify? This study provides a positive answer in a non-cooperative n-firm oligopoly model in which the firms determine levels of differentiated goods and abatement technologies. It first derives a Cournot–Nash equilibrium in which the firms maximize their profit and emit pollution under the ambient charge scheme, combining rewards from the total NPS concentration less than a given standard with the penalties above. The effect of the ambient charge is then analytically shown in homogeneous and heterogeneous duopoly and triopoly. Further, possible controllability is numerically examined in the case of n4. Full article
(This article belongs to the Special Issue Modern Trends in Game Theory and Optimal Control)
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