A Numerical Solution for Nash Differential Games Based on the Runge Kutta 4th-order Method

Authors

  • Abd El-Monem A. Megahed Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522,Egypt https://orcid.org/0009-0008-0430-6599
  • Nesreen M. Kamel Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522,
  • I. M. Hanafy Department of Mathematics and computer science, Faculty of Science, Port Said University, Egypt
  • Nora A. Omar Department of Mathematics and computer science, Faculty of Science, Port Said University, Egypt

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6007

Keywords:

Oopen-loop Nash differential game; , Runge-Kutta 4th order method; stability;, stability; , Uniform Convergence

Abstract

In this paper, we present a numerical solution for an open-loop Nash differential game modeling competition between two firms. Using the fourth-order Runge-Kutta method, we computed the numerical solution and analyzed the stability of the open-loop Nash equilibrium. Additionally, we examined the uniform convergence of the solution. Finally, an illustrative example is presented to clarify the results, accompanied by figures to illustrate the findings.

Downloads

Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Operational Research

License

Copyright (c) 2025 Abd El-Monem A. Megahed, Nesreen M. Kamel, I. M. Hanafy, Nora A. Omar

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

A Numerical Solution for Nash Differential Games Based on the Runge Kutta 4th-order Method. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6007. https://doi.org/10.29020/nybg.ejpam.v18i4.6007