International Journal of Systems Science and Applied Mathematics

Submit a Manuscript

Publishing with us to make your research visible to the widest possible audience.

Propose a Special Issue

Building a community of authors and readers to discuss the latest research and develop new ideas.

A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory

This Paper explores a new non-linear programming approach for determining mixed strategies in non-zero-sum games. Our approach leverages the power of non-linear optimization algorithms to solve the mixed strategy determination problem efficiently. We formulate the problem as a non-linear programming model, considering the individual player’s utility functions and the strategic interdependencies among them. The proposed approach offers accurately represents strategic interactions by incorporating non-linear objective functions and constraints. The proposed non-linear programming technique offers several advantages for solving game theory problems. Firstly, it enables the consideration of complex and nonlinear relationships among players' strategies, allowing for more realistic and nuanced modeling. Secondly, the technique offers flexibility in incorporating various types of constraints, including capacity limitations, budget constraints, or regulatory requirements, enhancing the applicability to real-world scenarios. Lastly, NLP algorithms provide efficient and robust optimization procedures, ensuring reliable solutions within reasonable time frames. We use MATLAB to solve the Non-Linear programming problem which gives us more accurate results. To demonstrate the effectiveness of the proposed technique, it can be applied to diverse game theory problems, such as auctions, bargaining, pricing decisions, and resource allocation. The results obtained through this approach offer insights into optimal strategies, equilibrium outcomes, and potential trade-offs, facilitating informed decision-making in strategic environments.

Equilibrium Concepts, Strategic Interactions, Nash Equilibrium, Pareto Optimal, Dominant Strategy, Mixed Strategy, Payoff Matrix, Saddle Point

APA Style

Md. Golam Robbani, Md. Asadujjaman, Md. Mehedi Hassan. (2023). A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory. International Journal of Systems Science and Applied Mathematics, 8(2), 17-22. https://doi.org/10.11648/j.ijssam.20230802.11

ACS Style

Md. Golam Robbani; Md. Asadujjaman; Md. Mehedi Hassan. A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory. Int. J. Syst. Sci. Appl. Math. 2023, 8(2), 17-22. doi: 10.11648/j.ijssam.20230802.11

AMA Style

Md. Golam Robbani, Md. Asadujjaman, Md. Mehedi Hassan. A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory. Int J Syst Sci Appl Math. 2023;8(2):17-22. doi: 10.11648/j.ijssam.20230802.11

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36 (1), 48-49.
2. von Neumann, J., & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
3. Taha H. A., Operations Research An Introduction, Prentice Hall of India Pvt. Ltd, New Delhi, 1999.
4. "Game Theory and Strategy" by Philip D. Straffin Jr. (Mathematical Association of America, 1993).
5. "Game Theory: A Nontechnical Introduction" by Morton D. Davis (Dover Publications, 1997).
6. "An Introduction to Game Theory" by Martin J. Osborne and Ariel Rubinstein (Oxford University Press, 1994).
7. Maskin, E., & Tirole, J. (1990). The principal-agent relationship with an informed principal, I: the case of private values. Econometrica, 58 (2), 379-409.
8. Harsanyi, J. C., & Selten, R. (1988). A General Theory of Equilibrium Selection in Games. MIT Press.
9. Myerson, R. B. (1981). Optimal Auction Design. Mathematics of Operations Research, 6 (1), 58-73.
10. Milgrom, P., & Roberts, J. (1990). Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica, 58 (6), 1255-1277.
11. Harsanyi, J. C. (1973). Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points. International Journal of Game Theory, 2 (1), 1-23.
12. Osborne, M. J., & Rubinstein, A. (1994). A Course in Game Theory. MIT Press.