‫‪Zero Sum GamesSolutions and Applications‬‬
‫اسن الطالثح‪ :‬ػْاطف أحوذ الؼزاتً‬
‫اششاف‪ :‬ا‪ .‬د‪.‬ػلً دمحم إتشاٍُن‬
‫لسن الشٌاضٍاخ‪-‬كلٍح الؼلْم‬
‫ماجستير–‪8002‬‬
‫ػٌذها ذْاجٌِا هشكلح صٌغ المشاس فً ظل ظشّف ذٌافسٍح ذرسن ترٌالص هْالف الورٌافسٍي ّذؼاسض‬
‫الوصالح فٍوا تٌٍِن‪ ،‬فإى ػولٍح اذخار المشاس ذصثح صؼثح فً هثل ُزٍ الظشّف الى ًرائج المشاس‬
‫ّأثشٍ ال ذؼروذ ػلى المشاس الورخز فمظ‪ ،‬تل ذرأثش تٌرائج المشاساخ الرً ٌرخزُا الورٌافسْى‪ّ .‬ذصثح‬
‫الوشكلح ًُ اذخار لشاس ٌرؼلك تالوصالح الورؼاسضح ّحل هثل ُزا الرؼاسض ُْ هحْس اُروام ًظشٌح‬
‫األلؼاب حٍث ذساػذ ًظشٌح األلؼاب فً فِن إسرشاذٍجٍاخ الورٌافسٍي ّذحلٍل احرواالذِا الوخرلفح‬
‫ّاذخار المشاس الوٌاسة لوماتلح الوْالف الوخرلفح للخصن‪ًّ .‬حي سْف ًمرصش ػلى هاٌسوى (ألؼاب‬
‫الوجوْع الصفشي لشخصٍي) حٍث لذم ُزا الثحث طشق حل األلؼاب راخ الوجوْع الصفشي‬
‫لشخصٍي ّرلك ترحذٌذ أفضل إسرشاذٍجٍح لكل هرٌافس ّذٌاّلد الذساسح كزلك حل ألؼاب الوجوْع‬
‫الصفشي تاسرخذام الثشهجح الخطٍح ّلوٌا تإػذاد تشًاهج لِا تلغح الفْذشاى لالسرفادج هٌَ لحل األلؼاب‬
‫راخ الحجن الكثٍش الرً ذرطلة كثٍش هي الجِذ ّالحساتاخ ّالْلد‪ .‬كوا ذرن الرشكٍز ػلى الشكل‬
‫الوْسغ لأللؼاب ّلوٌا توؼالجح هجوْػح هي األلؼاب تْاسطح شجشج اللؼة‪ .‬كوا ذن ذْضٍح الصلح تٍي‬
‫الشكل اإلسرشاذٍجً ّالشكل الوْسغ للؼثح‪.‬‬
Abstract:
When we encounter the problem of decision making under competent
circumstances shaped with the contradiction of players positions and the
contradictions of interrelated interests, the decision making process becomes
difficult under such circumstances, because the decision outcome and its
affect is not dependent of the said decision, instead, they are affected by the
results of the decisions taken by the players. Then the problem is in taking a
decision relevant to those contradicted interests and how to solve such
contradictions is the basic interest of the games theory. The games theory
helps in understanding the strategies of the players and analyzing the
strategies various possibilities and thus arriving at the proper decision to deal
with the different positions of the other player. We shall restrict our work on
to what so called (two-person zero- sum games). As this research has
suggested a solution method for the games of the zero sum for two persons,
via determination of the best strategy possible for each player. The study as
well dealt with the solution of the zero-sum games using the linear
programming. We prepared a program for that end- FORTRAN language in
order to benefit from it in solving the games of the bigger size which require
much efforts and calculations and time too. Great concentration was also
being given to the extensive configuration of the games, where we treated a
set of games by means of the play tree. We also attempted to clarify the
relation between the strategic form and the extensive form of game.