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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

On the graphical solution of matrix games

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pp. 1–11Online FirstMay 2026DOI: 10.47974/JIM-2427XML
Received:
01 Jul 2025
Published Online:
26 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2427
Pages:
1–11

Abstract

The graphical solution of 2 × 2, 2 × n, m × 2 matrix games is considered, and examples for applying this approach are presented. 

Keywords

Subject Classifications

91A0591A35

References

[1] Hadnan Akyar, and Emrah Akyar, “A graphical method for solving interval matrix games”, Abstract and Applied Analysis, vol. 2011, 17 pages, Article ID 260490 (2011). 
[2] S. Z. Alparslan Gök, R. Branzei, and S. Tijs, “Convex interval games”, Journal of Applied Mathematics and Decision Sciences, vol. 2009, pp. 1-14, Article ID 342089 (2009). 
[3] I. Khan, A. Aggarwal, A. Mehra, and S. Chandra, “Solving matrix games with Atanassov’s I-fuzzy goals via indeterminacy resolution approach”, Journal of Information and Optimization Sciences, vol. 38, no. 2, pp. 259-287 (2017), DOI: 10.1080/02522667.2016.1164999. 
[4] S. Kumar, D. S. N. Reddy, “Graphical solution of (n×m) matrix of a game theory”, European Journal of Operational Research, vol. 112, no. 2, pp. 467-471 (1999). 
[5] John von Neumann, “Zur Theorie der Gesellschaftsspiele”, Mathematische Annalen, vol. 100, no. 1, pp. 295-320 (1928) (in German). 
[6] John von Neumann, and Oskar Morgenstern, Theory of Games and Economic Behavior, 60-th anniversary ed., Princeton University Press, Princeton (2007). 
[7] Peter Morris, Introduction to Game Theory, Springer-Verlag, New York–Berlin–Heidelberg (1994). 
[8] S. M. Stefanov, Quantitaive Methods of Management, Heron Press, Sofia, (in Bulgarian) (2003). 
[9] S. M. Stefanov, “Minimization of a convex linear-fractional separable function subject to a convex inequality constraint or linear equality constraint and bounds on the variables”, Applied Mathematics Research Express AMRX, vol. 2006, no. 4, pp. 1-24 (2006), Article ID 36581. 
[10] S. M. Stefanov, “Solution of some convex separable resource allocation and production planning problems with bounds on the variables”, Journal of Interdisciplinary Mathematics, vol. 13, no. 5, pp. 541-569 (2010). 
[11] S. M. Stefanov, “Well-posedness and primal-dual analysis of some convex separable optimization problems”, Advances in Operations Research, vol. 2013, pp. 1-10 (2013), Article ID 279030, DOI:10.1155/2013/279030. 
[12] S. M. Stefanov, “On the application of iterative methods of nondifferentiable optimization to some problems of approximation theory”, Mathematical Problems in Engineering, vol. 2014, pp. 1-10, (2014), Article ID 165701. 
[13] S. M. Stefanov, “Characterization of the optimal solution of the convex generalized nonlinear transportation problem”, Journal of Interdisciplinary Mathematics, vol. 22, no. 5, pp. 745-756 (2019). 
[14] S. M. Stefanov, “Numerical solution of some systems of nonlinear algebraic equations”, Journal of Interdisciplinary Mathematics, vol. 24, no. 6, pp. 1545-1564 (2021). 
[15] Stefan M. Stefanov, Separable Optimization: Theory and Methods, Springer, New York, Springer Optimization and Its Applications, vol. 177, 2021. 
[16] S. M. Stefanov, “Numerical solution of systems of nonlinear equations defined by convex functions”, Journal of Interdisciplinary Mathematics, vol. 25, no. 4, pp. 951-962 (2022). 
[17] Stefan M. Stefanov, “On the solution of two-person zero-sum matrix games”, Journal of Information and Optimization Sciences, vol. 45, no. 3, pp. 649-657 (2024). 
[18] Stefan M. Stefanov, “Linear programming problems and matrix games”, Journal of Interdisciplinary Mathematics, vol. 27, no. 1, pp. 57-65 (2024). 
[19] Yuanhua Wang, Fuad E. Alsaadi, Zheng Liu, Xiaomeng Wu, and Xiyu Liu, “Matrix expression of Shapley value in graphical cooperative games”, Mathematical Problems in Engineering, vol. 2020, pp. 1-8 (2020), Article ID 2045654. 
[20] Jiuping Xu, and Liming Yao, “A class of two-person zero-sum matrix games with rough payoff”, International Journal of Mathematics and Mathematical Sciences, vol. 2010, pp. 1-22 (2010), Article ID 404792. 

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