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

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

Md. Golam Robbani, Md. Asadujjaman, Md. Mehedi Hassan

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

International Journal of Systems Science and Applied Mathematics, Volume 8, Issue 2, June 2023

Pages: 17-22

Received: Jun. 08, 2023

Accepted: Jul. 07, 2023

Published: Jul. 31, 2023

DOI: 10.11648/j.ijssam.20230802.11

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Abstract

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.

Keywords

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

To cite this article

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

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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.

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