Question
निम्नलिखित दो खिलाड़ी शून्य योग खेल को प्रमुखता सिद्धांत द्वारा 2×2 खेल में समानीत कीजिए और इस प्रकार खेल को हल कीजिए।
Answer :
Word Count : 836
src="https://latex.codecogs.com/svg.image?\begin{array}{c|cc}\multicolumn{3}{c}{\text{Player}B}\\&B_1&B_2\\\hline&space;A_1&1&-3\\A_2&3&5\\\text{Player}A\quad&space;A_3&-1&6\\A_4&4&1\\A_5&2&2\\A_6&-5&0\end{array}"> ChatGPT said: दिए गए शून्य योग 6 × 2 6×2 खेल को प्रमुखता सिद्धांत द्वारा 2 × 2 2×2 खेल में समानीत करके हल करने के लिए निम्नलिखित चरण अपनाएँगे: चरण 1: प्रमुख चालों को हटाना प्रमुखता सिद्धांत (dominance principle) के अनुसार, यदि कोई पंक्ति या स्तंभ किसी अन्य पंक्ति या स्तंभ से हमेशा बेहतर (या बराबर) होता है, तो उस पंक्ति या स्तंभ को हटा सकते हैं। (i) पंक्तियों का निरीक्षण खिलाड़ी A की रणनीतियों की तुलना करें: � 6 A 6 (-5, 0) को � 3 A 3 (-1, 6) द्वारा प्रमुख किया जाता है। क्योंकि − 1 > − 5 −1>−5 और 6 > 0 6>0, तो � 6 A 6 को हटा सकते हैं। � 5 A 5 (2, 2) को � 4 A 4 (4, 1) द्वारा प्रमुख किया जाता है। क्योंकि 4 > 2 4>2 और 1 ≤ 2 1≤2, तो � 5 A 5 को हटा सकते हैं। अब संशोधित पे-ऑफ मैट्रिक्स: � 1 � 2 � 1 1 − 3 � 2 3 5 � 3 − 1 6 � 4 4 1 A 1 A 2 A 3 A 4 B 1 1 3 −1 4 ___ ____ _______ _______ ___ ___ _____ __________ ___ ____.
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src="https://latex.codecogs.com/svg.image?\begin{array}{c|cc}\multicolumn{3}{c}{\text{Player}B}\\&B_1&B_2\\\hline&space;A_1&1&-3\\A_2&3&5\\\text{Player}A\quad&space;A_3&-1&6\\A_4&4&1\\A_5&2&2\\A_6&-5&0\end{array}"> ChatGPT said: दिए गए शून्य योग 6 × 2 6×2 खेल को प्रमुखता सिद्धांत द्वारा 2 × 2 2×2 खेल में समानीत करके हल करने के लिए निम्नलिखित चरण अपनाएँगे: चरण 1: प्रमुख चालों को हटाना प्रमुखता सिद्धांत (dominance principle) के अनुसार, यदि कोई पंक्ति या स्तंभ किसी अन्य पंक्ति या स्तंभ से हमेशा बेहतर (या बराबर) होता है, तो उस पंक्ति या स्तंभ को हटा सकते हैं। (i) पंक्तियों का निरीक्षण खिलाड़ी A की रणनीतियों की तुलना करें: � 6 A 6 (-5, 0) को � 3 A 3 (-1, 6) द्वारा प्रमुख किया जाता है। क्योंकि − 1 > − 5 −1>−5 और 6 > 0 6>0, तो � 6 A 6 को हटा सकते हैं। � 5 A 5 (2, 2) को � 4 A 4 (4, 1) द्वारा प्रमुख किया जाता है। क्योंकि 4 > 2 4>2 और 1 ≤ 2 1≤2, तो � 5 A 5 को हटा सकते हैं। अब संशोधित पे-ऑफ मैट्रिक्स: � 1 � 2 � 1 1 − 3 � 2 3 5 � 3 − 1 6 � 4 4 1 A 1 A 2 A 3 A 4 B 1 1 3 −1 4 ___ ____ _______ _______ ___ ___ _____ __________ ___ ____.
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