A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory
Md. Golam Robbani,
Md. Asadujjaman,
Md. Mehedi Hassan
Issue:
Volume 8, Issue 2, June 2023
Pages:
17-22
Received:
8 June 2023
Accepted:
7 July 2023
Published:
31 July 2023
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.
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 utilit...
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An Analysis of Solutions of Nonlinear Equations Using AI Inspired Mathematical Packages
Issue:
Volume 8, Issue 2, June 2023
Pages:
23-30
Received:
11 August 2023
Accepted:
29 August 2023
Published:
8 September 2023
Abstract: In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal choice among these tools based on their outcome when applied to solving nonlinear equations. This study addresses this question by undertaking a comparative analysis of three prominent mathematical software packages Python, Scilab, and MATLAB using two numerical approaches: Newton-Raphson and Secant. By employing the Newton-Raphson and Secant methods to solve five benchmark problems, this paper assesses the performance of the aforementioned mathematical tools. Notably, the outcomes underscore the competence of all three software options in yielding suitable approximations of the problem's root solutions. In particular, Python stands out for its ability to achieve this while utilizing the fewest iterations and minimizing computational time. As a result, among the three tools investigated, Python emerges as the most favorable choice, considering its efficiency and accuracy. Furthermore, this research validates the robustness of the Newton-Raphson approach over the Secant method, given its capability to efficiently converge to the solutions with the minimal iteration count across the benchmark problems. This finding highlights the superiority of the Newton-Raphson method as a more efficient and reliable technique for solving the considered benchmark problems.
Abstract: In the era of Artificial Intelligence (AI), achieving precise solutions for nonlinear equations has been considerably streamlined, thanks to the advancement of various mathematical tools designed for numerical computations. However, as the utilization of these mathematical software continues to rise, researchers are keen to ascertain the optimal ch...
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