MATRIX GAME EVALUATION IN GAME THEORY

Аннотация

Article games​ theory matrix games to the department dedicated to be , to work release and economy in the field conflicted processes mathematician modeling and solution methods seeing It turns out . Matrix of games main concepts , including achievement​ matrix , game lower and high prices , saddle point , maxmin and minimum strategies is explained . If the game saddle to the point has if not , mix strategies method using solution find process is described . Matrix games​ linear programming to the issue to bring methods and this optimal strategies in the process determination algorithms The article is cited . two examplethrough theoretical concepts practical solutions with is strengthened . Used literature list​ the topic deeper study for additional sources presented Article​ ​ mathematician programming and optimization in the field professionals , students and researchers for useful isconsidered . Keywords:Games​ ​ theory , matrix games , conflict processes , achievement matrix , saddle point , maxmin strategy , minimax strategy , game price , mixed strategies , linear programming ,optimalstrategy ,mathematics modeling ,economic issues ,workrelease​ Introduction . Processes research and optimal management – decision acceptance to doandsystems tooptimizescientific fields oriented .​ 1- Process research resources effective distribution for mathematician models , linear programming ,games​ theory andnetworks optimizationsuch as from methods uses . 2-Optimal management systems the most good management strategies determination with He is engaged in his work . main methods Pontryagin's Maximum principle and Bellman's dynamic programming . Research methodology In the article cited research methodology analysis to do for his/her content and from the structure come out , following main aspects seeing​ Let's go out . Article games​ theory matrix games to the department dedicated is a research methodology theoretical analysis , mathematics modeling and practical examples through solution to find is based on . Below methodology in detail analysis cited : Research general approach Theoretical basis : Article games​ theory main concepts ( achievement) matrix , saddle point , maxmin and page1273 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai minimax strategies , mixed strategies ) from explanation begins . These concepts conflicted processes economy and working release in the field modeling for basis to be service does . Mathematician Modeling : Research central methodology conflicted processes simplified mathematician as models ( games )​ to express is based on . In this process main factors into account is taken , the second level factors and out of consideration aside is left . Practical orientation : Article​ theoretical concepts practical through examples (example 1 and example 2) strengthen and help students this apply methods to real problems application opportunitygives . Literature analysis In the article cited used literature list​ games theory , mathematics programming and optimization in the field important sources cover takes . Below this of literature briefly analysis brought by : Akulich I.​ L.​ Mathematical programming in in examples and zadachax ​ - M .: Vysshaya school , 1996. Analysis : This book mathematician programming in the field practical issues and their to the solutions dedicated​ games​ ​ theory and linear to program related examples and exercises own inside takes . Book students and practitioners for comfortable theoretically​ ​ ​ knowledge practical skills with connects . In the article cited linear programming methods and matrix games​ solution algorithms this to the source based to be possible.Relevance : Article linear programming to the issues to bring process in explanation important contribution adds.Badalov FB Optimization theory and mathematician programming . “ Teacher ” , T. 1989. Analysis : Uzbek published in​ this book optimization theory and mathematician programming main concepts own inside takes . Local students​ for customized games​ ​ theory main principles in explanation important source as service does . The book Uzbek​ in the language in the environment written of the article local to the context compatibility provides.Relevance : In thearticle cited ofthe game price ,strategies and their mathematician modeling such as concepts this from the book taken to be possible . Kuznetsov A. V. , Novikova​ G. I. , Kholod​ N. I. Collection​ ​ task by mathematically speaking programming . Minsk , Vysheishaya school , 1985. Analysis : This source mathematician programming according to wide extensive issues set presented it will , that's it including games theory and linear programming with related issues own inside takes . The set practical orientation in the article cited examples and solutions to the structure Relevance : In the arti