‫ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻲ ﺷﺮﻳﻒ‬
‫ﺩﺍﻧﺸﮑﺪﻩ ﻣﻬﻨﺪﺳﻲ ﮐﺎﻣﭙﻴﻮﺗﺮ‬
‫ﻣﻘﺎﻟﻪ ﺩﺭﺱ ﻧﻈﺮﻳﻪ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺑﺎﺯﻱﻫﺎ‬
‫ﻋﻨﻮﺍﻥ‪:‬‬
‫ﮐﺎﺭﺑﺮﺩ ﻫﺎﻱ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﺩﺭ ﻣﺴﺎﺋﻞ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ‬
‫ﻧﮕﺎﺭﺵ‪:‬‬
‫ﻣﺴﻌﻮﺩ ﻓﺮﻳﻮﺭ‬
‫ﺍﺳﺘﺎﺩ ﺩﺭﺱ‬
‫ﺩﮐﺘﺮ ﺻﻔﺮﻱ‬
‫ﺒﻬﻤﻥ ‪1387‬‬
‫ﭼﮑﻴﺪﻩ ‪:‬‬
‫ﺑﺎ ﮔﺬﺷﺖ ﺑﻴﺶ ﺍﺯ ﻧﻴﻢ ﻗﺮﻥ ﺍﺯ ﻣﻌﺮﻓﻲ ﻣﻔﺎﻫﻴﻢ ﭘﺎﻳﻪ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﺗﻮﺳﻂ ﺟﺎﻥ ﻧﺶ ﻭ ﻭﻥ ﻧﻮﻳﻤﺎﻥ ‪ ،‬ﺍﺧﻴﺮﺍ ﺷﺎﻫﺪ‬
‫ﺭﺷﺪ ﻗﺎﺑﻞ ﺗﻮﺟﻪ ﺗﺤﻘﻴﻘﺎﺕ ﺩﺭ ﺯﻣﻴﻨﻪ ﮐﺎﺭﺑﺮﺩﻫﺎﻱ ﺍﻳﻦ ﻧﻈﺮﻳﻪ ﺩﺭ ﺷﺒﮑﻪﻫﺎ ﻭ ﺑﺨﺼﻮﺹ ﻣﺪﻝ ﺳﺎﺯﻱ ﺭﻓﺘﺎﺭ ﮐﺎﺭﺑﺮﺍﻥ‬
‫ﺷﺒﮑﻪﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ ﻭ ﺑﻲﺳﻴﻢ ﻫﺴﺘﻴﻢ‪ .‬ﮐﺎﺭﺑﺮﺍﻥ ﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎ ﻣﺠﻤﻮﻋﻪ ﺍﻱ ﺍﺯ ﺍﻧﺘﺨﺎﺏ ﻫﺎﻱ ﻣﻤﮑﻦ ﭘﻴﺶ ﺭﻭﻱ‬
‫ﺧﻮﺩ ﺩﺍﺭﻧﺪﮐﻪ ﻣﻤﮑﻦ ﺍﺳﺖ ﺩﺭ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﻫﺎﻱ ﺧﻮﺩ ﺳﻮﺩ ﺷﺨﺼﻲ ﺭﺍ ﺑﻪ ﻣﻨﺎﻓﻊ ﮐﻠﻲ ﺷﺒﮑﻪ ﻭ ﺳﺎﻳﺮ ﮐﺎﺭﺑﺮﺍﻥ‬
‫ﺗﺮﺟﻴﺢ ﺩﻫﻨﺪ‪ .‬ﺍﺯ ﺍﻳﻦ ﺭﻭ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎﻱ ﻏﻴﺮ ﺗﻌﺎﻭﻧﻲ ﻣﻲ ﺗﻮﺍﻧﺪ ﺍﺑﺰﺍﺭ ﻣﻨﺎﺳﺒﻲ ﺑﺮﺍﻱ ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﮔﺮﻩ ﻫﺎﻱ‬
‫ﺧﻮﺩ ﺧﻮﺍﻩ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎ ﺑﺎﺷﺪ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﺍﻳﻦ ﺑﻪ ﮐﻤﮏ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻣﻲ ﺗﻮﺍﻥ ﺍﻗﺪﺍﻡ ﺑﻪ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻳﻲ‬
‫ﺑﺮﺍﻱ ﺷﺒﮑﻪ ﻫﺎ ﻧﻤﻮﺩ ﮐﻪ ﺣﺘﻲ ﺑﺪﻭﻥ ﮐﻨﺘﺮﻝ ﻭ ﻣﺪﺭﻳﺖ ﻣﺮﮐﺰﻱ ﺗﻤﺎﻡ ﮔﺮﻩ ﻫﺎ ﺍﻧﮕﻴﺰﻩ ﺍﻱ ﺑﺮﺍﻱ ﺗﺨﻄﻲ ﺍﺯ ﺁﻥ ﻫﺎ‬
‫ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺍﺑﺘﺪﺍ ﺑﺎ ﺫﮐﺮ ﭼﻨﺪ ﻣﺜﺎﻝ ﺳﺎﺩﻩ‪ ،‬ﺍﻳﺪﻩ ﻣﺪﻝ ﺳﺎﺯﻱ ﻣﺴﺎﺋﻞ ﺷﺒﮑﻪ ﺑﻪ ﮐﻤﮏ ﻧﻈﺮﻳﻪ‬
‫ﺑﺎﺯﻱ ﺭﺍ ﻣﻌﺮﻓﻲ ﻭ ﺳﭙﺲ ﺑﻪ ﺑﺮﺭﺳﻲ ﺟﺰﺋﻲ ﺗﺮ ﭼﻨﺪ ﺑﺎﺯﻱ ﻣﻬﻢ ﻣﻲ ﭘﺮﺩﺍﺯﻳﻢ‪ .‬ﻫﺪﻑ ﺍﺯ ﻧﮕﺎﺭﺵ ﺍﻳﻦ ﻣﻘﺎﻟﻪ‬
‫ﺁﺷﻨﺎﺳﺎﺯﻱ ﺩﺍﻧﺸﺠﻮﻳﺎﻥ ﺭﺷﺘﻪ ﺑﺮﻕ ﻭ ﮐﺎﻣﭙﻴﻮﺗﺮ ﺑﺎ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺟﺪﻳﺪ ﺗﺤﻘﻴﻘﺎﺗﻲ ﺑﻮﺩﻩ ﺍﺳﺖ‪.‬‬
‫ﻓﻬﺮﺳﺖ ﻣﻄﺎﻟﺐ‬
‫‪ -1‬ﻣﻘﺪﻣﻪ‬
‫‪1‬‬
‫‪ -2‬ﺑﺮﺭﺳﻲ ﭼﻨﺪ ﺑﺎﺯﻱ ﺍﺳﺘﺎﺗﻴﮏ ﺳﺎﺩﻩ ﺑﺮﺍﻱ ﺷﺒﮑﻪ ﻫﺎ‬
‫‪2‬‬
‫‪ 1-2‬ﺑﺎﺯﻱ ﺍﺭﺳﺎﻝ ﻣﺘﻘﺎﺑﻞ ﺩﺍﺩﻩ ﻫﺎ ‪2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 2-2‬ﺑﺎﺯﻱ ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻣﺸﺘﺮﮎ ﺑﻪ ﻣﻘﺼﺪ ‪3 . . . . . . . . . . . . . . . .‬‬
‫‪ 3-2‬ﺑﺎﺯﻱ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ‪3 . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 4-2‬ﺑﺎﺯﻱ ﺍﻳﺠﺎﺩ ﺍﺧﺘﻼﻝ ﺩﺭ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ‪4 . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ -3‬ﺻﺤﺖ ﻓﺮﺿﻴﺎﺕ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ‬
‫‪5‬‬
‫‪ 1-3‬ﻓﺮﺽ ﻋﻘﻼﻧﻴﺖ ‪5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 2-3‬ﻓﺮﺽ ﺍﻃﻼﻋﺎﺕ ﮐﺎﻣﻞ‪5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 3-3‬ﻓﺮﺽ ﻧﺎﻣﺘﻨﺎﻫﻲ ﺑﻮﺩﻥ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﻫﺎ ‪6 . . . . . . . . . . . . . .‬‬
‫‪ 4-3‬ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ‪6 . . . . . . . . . . . . . . . . .‬‬
‫‪ 5-3‬ﻓﺮﺽ ﺧﻮﺩ ﺧﻮﺍﻫﻲ‪. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .‬‬
‫‪ -4‬ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ‬
‫‪6‬‬
‫‪7‬‬
‫‪ 1-4‬ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ‪7 . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 2-4‬ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﮐﻨﺘﺮﻝ ﺗﻮﺍﻥ ‪. . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ -5‬ﺍﺷﺎﺭﻩ ﺍﻱ ﺑﻪ ﭼﻨﺪ ﺑﺎﺯﻱ ﻣﻬﻢ ﺩﻳﮕﺮ‬
‫‪9‬‬
‫‪11‬‬
‫‪ 1-5‬ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺩﺭ ﺷﺒﮑﻪ ‪11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 2-5‬ﺑﺎﺯﻱ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ ‪11 . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .‬‬
‫‪ 3-5‬ﺑﺎﺯﻱ ﻣﺪﻳﺮﻳﺖ ﺍﻋﺘﺒﺎﺭ ﺩﺭ ﺷﺒﮑﻪ ‪11 . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ 4-5‬ﺑﺎﺯﻱ ﮐﻨﺘﺮﻝ ﺟﺮﻳﺎﻥ ﺩﺭ ﺷﺒﮑﻪ‪12 . . . . . . . . . . . . . . . . . . . . . . . . . . .‬‬
‫‪ -6‬ﻧﺘﻴﺠﻪ ﮔﻴﺮﻱ‬
‫‪12‬‬
‫‪ -7‬ﻣﺮﺍﺟﻊ‬
‫‪13‬‬
‫‪ -1‬ﻣﻘﺪﻣﻪ‬
‫ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﻋﻨﻮﺍﻥ ﻋﻠﻢ ﻣﺪﻝ ﺳﺎﺯﻱ ﻭ ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻧﺪﻩ ﺗﻌﺮﻳﻒ ﮐﺮﺩ‪ .‬ﻫﺮ ﺑﺎﺯﻱ ﺷﺎﻣﻞ‬
‫ﻣﺠﻤﻮﻋﻪ ﺍﻱ ﺍﺯ ﺑﺎﺯﻳﮑﻨﺎﻥ‪ ،‬ﻣﺠﻤﻮﻋﻪ ﺍﻱ ﺍﺯ ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎﻱ ﻣﻤﮑﻦ ﺑﺮﺍﻱ ﻫﺮﻳﮏ ﺍﺯ ﺁﻥ ﻫﺎ ﻭ ﺑﺎﻻﺧﺮﻩ ﻣﺠﻤﻮﻋﻪ ﺍﺯ ﺗﻮﺍﺑﻊ ﺳﻮﺩ ﺑﺮﺍﻱ ﻫﺮ‬
‫ﺑﺎﺯﻳﮑﻦ ﻧﺴﺒﺖ ﺑﻪ ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎﻱ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺎﺯﻱ ﻣﻲ ﺷﻮﺩ‪ .‬ﺍﻳﻦ ﻧﻈﺮﻳﻪ ﮐﻪ ﺑﻴﺶ ﺍﺯ ﻧﻴﻢ ﻗﺮﻥ ﭘﻴﺶ ﻭ ﻫﻤﺰﻣﺎﻥ ﺑﺎ ﻣﻘﺎﻻﺕ ﻭﻥ ﻧﻴﻮﻣﻦ ﻭ‬
‫ﺟﺎﻥ ﻧﺶ ﭘﺎﻳﻪ ﺭﻳﺰﻱ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺗﺎ ﮐﻨﻮﻥ ﻋﻤﺪﺗﺎ ﺩﺭ ﺑﺮﺭﺳﻲ ﻣﺴﺎﺋﻠﻲ ﺍﺯ ﻋﻠﻮﻡ ﺍﻗﺘﺼﺎﺩﻱ ﻭ ﺳﻴﺎﺳﻲ ﺑﻪ ﮐﺎﺭ ﺭﻓﺘﻪ ﺍﺳﺖ‪.‬‬
‫ﻳﮑﻲ ﺍﺯ ﺍﻫﺪﺍﻑ ﺍﻳﻦ ﻧﻈﺮﻳﻪ‪ ،‬ﭘﻴﺶ ﺑﻴﻨﻲ ﭘﻴﺶ ﺁﻣﺪﻫﺎﻱ ﻣﺤﺘﻤﻞ ﺑﺮﺍﻱ ﺑﺎﺯﻱ ﻫﺎﻱ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﺍﺳﺖ‪ .‬ﻏﺎﻟﺒﺎ ﺑﻪ ﺩﻧﺒﺎﻝ ﭘﺎﺳﺨﻲ ﺑﺮﺍﻱ‬
‫ﺍﻳﻦ ﭘﺮﺳﺶ ﻫﺴﺘﻴﻢ ﮐﻪ ﺑﺎ ﻓﺮﺽ ﻋﻘﻼﻧﻴﺖ ﺑﺮﺍﻱ ﺑﺎﺯﻳﮑﻨﺎﻥ‪ ،‬ﺁﻥ ﻫﺎ ﭼﻪ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺑﺮﺍﻱ ﺣﺪﺍﮐﺜﺮ ﮐﺮﺩﻥ ﺳﻮﺩ ﺧﻮﺩ ﺩﺭ ﺑﺎﺯﻱ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ‬
‫ﻋﮑﺲ ﺍﻟﻌﻤﻞ ﻫﺎﻱ ﻣﻤﮑﻦ ﺑﺮﺍﻱ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ‪ ،‬ﺍﻧﺘﺨﺎﺏ ﺧﻮﺍﻫﻨﺪ ﮐﺮﺩ؟ ﻣﺘﺪﺍﻭﻝ ﺗﺮﻳﻦ ﭘﺎﺳﺦ ﺑﻪ ﺍﻳﻦ ﺳﻮﺍﻝ‪ ،‬ﻧﻘﺎﻁ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱﻫﺎ‬
‫ﻫﺴﺘﻨﺪ ﮐﻪ ﺩﺭ ﺁﻥﻫﺎ ﻫﻴﭽﻴﮏ ﺍﺯ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﻪ ﺗﻨﻬﺎﻳﻲ ﻧﻤﻲ ﺗﻮﺍﻧﺪ ﺑﺎ ﺗﻐﻴﻴﺮ ﺍﺳﺘﺮﺍﺗﮋﻱ‪ ،‬ﺳﻮﺩ ﺧﻮﺩ ﺭﺍ ﺍﻓﺰﺍﻳﺶ ﺩﻫﺪ‪ .‬ﺍﻟﺒﺘﻪ ﺑﺎﻳﺪ ﺍﺷﺎﺭﻩ ﮐﺮﺩ‬
‫ﮐﻪ ﺷﺎﺧﻪ ﺩﻳﮕﺮﻱ ﺍﺯ ﺍﻳﻦ ﻧﻈﺮﻳﻪ ﻳﻌﻨﻲ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱﻫﺎﻱ ﺗﻌﺎﻭﻧﻲ ﺑﻪ ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱﻫﺎﻳﻲ ﻣﻲﭘﺮﺩﺍﺯﺩ ﮐﻪ ﺩﺭ ﺁﻥﻫﺎ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻃﺒﻖ ﺗﻮﺍﻓﻘﺎﺕ‬
‫ﻗﺒﻠﻲ ﻭ ﻳﺎ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺳﻮﺩ ﺟﻤﻌﻲ ﺭﻓﺘﺎﺭ ﻣﻲﮐﻨﻨﺪ‪.‬‬
‫ﺩﺭ ﺳﺎﻝ ﻫﺎﻱ ﺍﺧﻴﺮ ﻭ ﻫﻤﺰﻣﺎﻥ ﺑﺎ ﮔﺴﺘﺮﺵ ﺭﻭﺯ ﺍﻓﺰﻭﻥ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ‪ ،‬ﺑﻪ ﺩﻻﻳﻞ ﺍﻗﺘﺼﺎﺩﻱ ﺍﺯ ﺟﻤﻠﻪ ﻋﺪﻡ ﻧﻴﺎﺯ ﺑﻪ ﺍﻳﺴﺘﮕﺎﻩﻫﺎﻱ‬
‫ﻣﺮﮐﺰﻱ ﺑﺮﺍﻱ ﻣﺪﻳﺮﻳﺖ ﺭﻓﺘﺎﺭ ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ‪ ،‬ﻧﻴﺎﺯ ﺑﻪ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﻭﻳﮋﻩ ﺍﻱ ﺑﺮﺍﻱ ﮐﻨﺘﺮﻝ ﺭﻓﺘﺎﺭ ﮔﺮﻩﻫﺎﻱ ﻣﺴﺘﻘﻞ ﻭ ﺧﻮﺩ‬
‫ﻣﺨﺘﺎﺭ ﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎ ﺑﻮﺟﻮﺩ ﺁﻣﺪﻩ ﺍﺳﺖ‪ .‬ﺍﺯ ﺟﻤﻠﻪ ﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺷﺒﮑﻪ ﻫﺎﻱ ﺳﻨﺴﻮﺭ‪ ،‬ﺷﺒﮑﻪ ﻫﺎﻱ ﻫﻤﻪ ﺟﺎﻳﻲ ﻣﺎﻧﻨﺪ‬
‫ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻴﻦ ﺧﻮﺩﺭﻭ ﻫﺎ ﻭ ﺷﺒﮑﻪ ﻫﺎﻱ ﭘﺮﺩﺍﺯﺵ ﺗﻮﺯﻉ ﺷﺪﻩ ﺍﺷﺎﺭﻩ ﮐﺮﺩ‪.‬‬
‫ﺑﻪ ﺗﺎﺯﮔﻲ ﺍﻳﻦ ﻧﻈﺮﻳﻪ ﺩﺭ ﺑﺮﺭﺳﻲ ﻭ ﻣﺪﻝ ﺳﺎﺯﻱ ﻣﺴﺎﺋﻠﻲ ﺍﺯ ﺷﺒﮑﻪ ﻫﺎ ﻧﻴﺰ ﺑﻪ ﮐﺎﺭ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ‪ ،‬ﻫﻤﺎﻥ‬
‫ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺴﺘﻨﺪ ﻭ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺍﻳﻦ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺷﺎﻣﻞ ﺍﻧﺘﺨﺎﺏ ﺗﻮﺍﻥ ﺍﺭﺳﺎﻟﻲ‪ ،‬ﭘﺎﺭﺍﻣﺘﺮ ﻫﺎﻱ ﮐﻨﺘﺮﻝ ﺍﻧﺒﺎﺷﺘﮕﻲ ﺩﺭ ﺷﺒﮑﻪ ﻣﺎﻧﻨﺪ‬
‫ﻣﺪﺕ ﺯﻣﺎﻥ ﻋﻘﺐ ﮔﺮﺩ‪ ،‬ﺍﻧﺘﺨﺎﺏ ﻧﻮﻉ ﻣﺪﻭﻻﺳﻴﻮﻥ‪ ،‬ﻧﺮﺥ ﮐﺪﻳﻨﮓ‪ ،‬ﺗﻌﻴﻴﻦ ﻣﺴﻴﺮﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺩﺭ ﺷﺒﮑﻪ‪ ،‬ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ‬
‫ﻫﺎﻱ ﺳﺎﻳﺮ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻭ ﺑﺴﻴﺎﺭﻱ ﺩﻳﮕﺮ ﺍﺯ ﭘﺎﺭﺍﻣﺘﺮ ﻫﺎﻱ ﺷﺒﮑﻪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﺑﺪﻟﻴﻞ ﻋﺪﻡ ﻣﺪﻳﺮﻳﺖ ﻣﺮﮐﺰﻱ‪ ،‬ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﺑﺮﺍﻱ ﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ ﺑﺎﻳﺪ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺑﺎﺷﺪ ﮐﻪ ﺣﺘﻲ ﺑﺎ ﻭﺟﻮﺩ ﺭﻓﺘﺎﺭ‬
‫ﺧﻮﺩﺧﻮﺍﻫﺎﻧﻪ ﻭ ﺗﺮﺟﻴﺢ ﺩﺍﺩﻥ ﺳﻮﺩ ﺷﺨﺼﻲ ﻧﺴﺒﺖ ﺑﻪ ﺳﻮﺩ ﺟﻤﻌﻲ‪ ،‬ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﻴﭻ ﺗﻤﺎﻳﻠﻲ ﺑﻪ ﺗﺨﻄﻲ ﺍﺯ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﺍﺭﺍﺋﻪ‬
‫ﺷﺪﻩ ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ‪ .‬ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﺍﺷﺎﺭﻩ ﺷﺪ‪ ،‬ﻧﻘﺎﻁ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱ ﻫﺎ ﺩﺍﺭﺍﻱ ﺍﻳﻦ ﻭﻳﮋﮔﻲ ﻣﻬﻢ ﻫﺴﺘﻨﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﻣﻲ ﺑﻴﻨﻴﻢ ﮐﻪ‬
‫ﭼﮕﻮﻧﻪ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﻣﻲﺗﻮﺍﻧﺪ ﻣﺎﻧﻨﺪ ﺍﺑﺰﺍﺭﻱ ﺩﺭ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﻣﻘﺎﻭﻡ ﺑﺮﺍﻱ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ‪ ،‬ﻣﻬﻨﺪﺳﺎﻥ ﺷﺒﮑﻪ ﺭﺍ ﻳﺎﺭﻱ‬
‫ﺭﺳﺎﻧﺪ‪.‬‬
‫ﭘﺲ ﺍﺯ ﺍﻳﻦ ﻣﻘﺪﻣﻪ ﻭ ﺩﺭ ﺑﺨﺶ ﺩﻭﻡ ﻣﻘﺎﻟﻪ‪ ،‬ﺑﺎ ﺫﮐﺮ ﭼﻬﺎﺭ ﻣﺜﺎﻝ ﺳﺎﺩﻩ‪ ،‬ﺍﻳﺪﻩ ﻣﺪﻝ ﺳﺎﺯﻱ ﻣﺴﺎﺋﻞ ﻣﺮﺑﻮﻁ ﺑﻪ ﻻﻳﻪ ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺷﺒﮑﻪ ﺑﻪ‬
‫ﮐﻤﮏ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺭﺍ ﻣﻄﺮﺡ ﻣﻲﮐﻨﻴﻢ‪ .‬ﺩﺭ ﺑﺨﺶ ﺳﻮﻡ ﺻﺤﺖ ﻓﺮﺿﻴﺎﺕ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺩﺭ ﻣﻮﺭﺩ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﺑﺮﺭﺳﻲ ﺧﻮﺍﻫﻨﺪ‬
‫ﺷﺪ‪ .‬ﺩﺭ ﺑﺨﺶ ﭼﻬﺎﺭﻡ ﺩﻭ ﺑﺎﺯﻱ ﻣﻬﻢ ﺷﺒﮑﻪﻫﺎ ﻳﻌﻨﻲ ﺑﺎﺯﻱ ﭘﻲﺩﺭﭘﻲ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ﻭ ﺑﺎﺯﻱ ﭘﻲﺩﺭﭘﻲ ﮐﻨﺘﺮﻝ ﺗﻮﺍﻥ ﺑﻪ‬
‫ﻃﻮﺭ ﺟﺰﺋﻲ ﺗﺮ ﺑﺮﺭﺳﻲ ﺧﻮﺍﻫﻨﺪ ﺷﺪ‪ .‬ﺩﺭ ﻓﺼﻞ ﭘﻨﺠﻢ ﻧﻴﺰ ﺍﺷﺎﺭﻩ ﺍﻱ ﮔﺬﺭﺍ ﺑﻪ ﭼﻨﺪ ﺑﺎﺯﻱ ﺩﻳﮕﺮ ﺷﺒﮑﻪ ﻫﺎ ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ‪.‬‬
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‫ﺑﺎ ﺍﻳﻨﮑﻪ ﮐﻤﺘﺮ ﺍﺯ ﺩﻩ ﺳﺎﻝ ﺍﺯ ﺁﻏﺎﺯ ﮐﺎﺭ ﺑﺮ ﺭﻭﻱ ﮐﺎﺭﺑﺮﺩ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺩﺭ ﺷﺒﮑﻪﻫﺎ ﻣﻲﮔﺬﺭﺩ‪ ،‬ﺭﺷﺪ ﺳﺮﻳﻊ ﻣﻘﺎﻻﺕ ﻭ ﻫﻤﭽﻨﻴﻦ ﺑﺮﮔﺰﺍﺭﻱ‬
‫ﮐﻨﻔﺮﺍﻧﺲ ﻫﺎﻱ ﻋﻠﻤﻲ ﺳﺎﻻﻧﻪ ﺩﺭ ﺍﻳﻦ ﺯﻣﻴﻨﻪ‪ ،‬ﻫﻤﮕﻲ ﮔﻮﻳﺎﻱ ﺍﻫﻤﻴﺖ ﺭﻭﺯﺍﻓﺰﻭﻥ ﺍﻳﻦ ﻧﻈﺮﻳﻪ ﺩﺭ ﻣﺪﻝ ﺳﺎﺯﻱ ﻣﺴﺎﺋﻞ ﺷﺒﮑﻪﻫﺎ ﻭ ﺑﺨﺼﻮﺹ‬
‫ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲﺳﻴﻢ ﻧﺎﻣﺘﻤﺮﮐﺰ ﻫﺴﺘﻨﺪ‪ .‬ﻭﻳﮋﮔﻲ ﺟﺎﻟﺐ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺗﺤﻘﻴﻘﺎﺗﻲ ﻣﺸﺘﺮﮎ ﺑﻮﺩﻥ ﺁﻥ ﺑﻴﻦ ﺭﺷﺘﻪ ﻫﺎﻳﻲ ﻣﺎﻧﻨﺪ ﻣﺨﺎﺑﺮﺍﺕ‪،‬‬
‫ﻋﻠﻮﻡ ﮐﺎﻣﭙﻴﻮﺗﺮ‪ ،‬ﺭﻳﺎﺿﻲ ﻭ ﮐﻨﺘﺮﻝ ﺍﺳﺖ‪ .‬ﺍﻣﻴﺪﻭﺍﺭﻡ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺳﻬﻢ ﻫﺮﭼﻨﺪ ﮐﻮﭼﮑﻲ ﺩﺭ ﺁﺷﻨﺎﻳﻲ ﺩﺍﻧﺸﺠﻮﻳﺎﻥ ﺍﻳﻦ ﺭﺷﺘﻪ ﻫﺎ ﺑﺎ ﺍﻳﺪﻩ ﻫﺎﻱ‬
‫ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺟﺪﻳﺪ ﺗﺤﻘﻴﻘﺎﺗﻲ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪.‬‬
‫‪ -2‬ﺑﺮﺭﺳﻲ ﭼﻨﺪ ﺑﺎﺯﻱ ﺍﺳﺘﺎﺗﻴﮏ ﺳﺎﺩﻩ ﺑﺮﺍﻱ ﺷﺒﮑﻪ ﻫﺎ‬
‫ﺩﺭ ﺍﻳﻦ ﺑﺨﺶ ﻣﻲ ﺧﻮﺍﻫﻴﻢ ﺑﺎ ﺫﮐﺮ ‪ 4‬ﻣﺜﺎﻝ ﺳﺎﺩﻩ ﺍﺯ ﺑﺎﺯﻱ ﻫﺎﻱ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﻱ ﺍﻳﺪﻩ ﺑﻪ ﮐﺎﺭﮔﻴﺮﻱ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺩﺭ ﺑﺮﺭﺳﻲ ﻣﺴﺎﺋﻠﻲ ﺍﺯ‬
‫ﺷﺒﮑﻪ ﻫﺎ ﺭﺍ ﻧﺸﺎﻥ ﺩﻫﻴﻢ‪ .‬ﺍﻳﻦ ﻣﺜﺎﻝ ﻫﺎ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﺷﺪﻩ ﺍﻧﺪ ﮐﻪ ﺷﺎﻣﻞ ﻣﺴﺎﺋﻠﻲ ﺍﺯ ‪ 3‬ﻻﻳﻪ ﭘﺎﻳﻴﻨﻲ ﺷﺒﮑﻪ ﻳﻌﻨﻲ ﻻﻳﻪ ﻓﻴﺰﻳﮑﻲ‪ ،‬ﻻﻳﻪ‬
‫ﮐﻨﺘﺮﻝ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﻣﺤﻴﻂ ﻭ ﻻﻳﻪ ﺷﺒﮑﻪ )ﻣﺴﻴﺮ ﻳﺎﺑﻲ( ﺑﺸﻮﻧﺪ‪.‬‬
‫‪ -1-2‬ﺑﺎﺯﻱ ﺍﺭﺳﺎﻝ ﻣﺘﻘﺎﺑﻞ ﺩﺍﺩﻩ ﻫﺎ‬
‫ﻓﺮﺽ ﮐﻨﻴﺪ ﺩﻭ ﻓﺮﺳﺘﻨﺪﻩ ‪ p1‬ﻭ ‪ p2‬ﺑﺨﻮﺍﻫﻨﺪ ﺑﻪ ﺗﺮﺗﻴﺐ ﺑﻪ ﺩﻭ ﮔﻴﺮﻧﺪﻩ ‪ r1‬ﻭ ‪ r2‬ﺑﺴﺘﻪ ﺩﺍﺩﻩ ﺧﻮﺩ ﺭﺍ ﺍﺭﺳﺎﻝ ﮐﻨﻨﺪ ﻭﻟﻲ ﻫﻴﭽﻴﮏ ﻧﺘﻮﺍﻧﻨﺪ‬
‫ﺑﺪﻭﻥ ﮐﻤﮏ ﺩﻳﮕﺮﻱ ﺍﻳﻦ ﮐﺎﺭ ﺭﺍ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ‪ .‬ﺍﻳﻦ ﻭﺿﻌﻴﺖ ﺩﺭ ﺷﮑﻞ ﺯﻳﺮ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫ﺑﺮﺍﻱ ﻣﺪﻝ ﺳﺎﺯﻱ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﺑﺎﺯﻱ ﺩﻭ ﻓﺮﺳﺘﻨﺪﻩ ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺎﺯﻱ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﻫﺮﻳﮏ ‪ 2‬ﺍﺳﺘﺮﺍﺗﮋﻱ‬
‫ﺩﺍﺭﻧﺪ‪ :‬ﺭﺳﺎﻧﺪﻥ ﺑﺴﺘﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺩﻳﮕﺮ)‪ (F‬ﺑﻪ ﻣﻘﺼﺪ ﻳﺎ ﻧﻔﺮﺳﺘﺎﺩﻥ )‪ .(D‬ﺑﺮﺍﻱ ﺳﺎﺩﻩ ﺳﺎﺯﻱ ﺑﺎﺯﻱ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﻱ ﺍﺳﺘﺎﺗﻴﮏ ﺩﺭ‬
‫ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺍﺯ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺩﻳﮕﺮ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻃﻼﻋﻲ ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﻓﺮﺽ ﻣﻲ ﮐﻨﻴﻢ ﺳﻮﺩ ﻧﺎﺷﻲ ﺍﺯ‬
‫ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﺑﺴﺘﻪ ﺑﻪ ﻣﻘﺼﺪ ﺑﺮﺍﻱ ﻫﺮ ﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ‪ 1‬ﻭﺍﺣﺪ ﺑﻮﺩﻩ ﻭ ﻫﺰﻳﻨﻪ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﺩﻳﮕﺮ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﻣﻘﺼﺪﺵ ﻣﻘﺪﺍﺭ ﺛﺎﺑﺖ‬
‫‪ << 1‬ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﻫﺰﻳﻨﻪ ﻣﺮﺑﻮﻁ ﺑﻪ ﺗﻮﺍﻥ ﻣﺼﺮﻓﻲ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﺩﺍﺩﻩ ﺍﺳﺖ )ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ﺳﻴﻤﻲ ﺑﻪ ﺩﻟﻴﻞ ﻋﺪﻡ ﻭﺟﻮﺩ‬
‫ﻣﺤﺪﻭﺩﻳﺖ ﺗﻮﺍﻥ‪ ،‬ﺍﻳﻦ ﻫﺰﻳﻨﻪ ﻗﺎﺑﻞ ﺻﺮﻑ ﻧﻈﺮﺍﺳﺖ( ‪.‬ﻓﺮﻡ ﺍﺳﺘﺮﺍﺗﮋﻳﮏ ﺍﻳﻦ ﺑﺎﺯﻱ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
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‫ﺗﻌﺎﺩﻝ ﻧﺶ ﺍﻳﻦ ﺑﺎﺯﻱ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺳﺎﺩﮔﻲ ﺍﺯ ﺭﻭﺵ ﺑﻬﺘﺮﻳﻦ ﭘﺎﺳﺦ ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ :‬ﺑﺮﺍﻱ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻣﺴﺘﻘﻞ ﺍﺯ ﺍﺳﺘﺮﺍﺗﮋﻱ‬
‫ﻓﺮﺳﺘﻨﺪﻩ ﻣﻘﺎﺑﻞ ﻋﺪﻡ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ )‪ (D‬ﺑﻬﺘﺮﻳﻦ ﭘﺎﺳﺦ ﺍﺳﺖ‪ .‬ﭘﺲ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﺯﻭﺝ ﺍﺳﺘﺮﺍﺗﮋﻱ )‪ (D,D‬ﺧﻮﺍﻫﺪ ﺑﻮﺩ ﮐﻪ ﺳﻮﺩ )‪ (0,0‬ﺭﺍ ﺑﺮﺍﻱ‬
‫ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺑﻪ ﺩﻧﺒﺎﻝ ﺧﻮﺍﻫﺪ ﺩﺍﺷﺖ‪ .‬ﺍﻳﻦ ﻣﺜﺎﻝ ﻣﺮﺑﻮﻁ ﺑﻪ ﻻﻳﻪ ﺷﺒﮑﻪ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱ ﺑﻬﻴﻨﻪ ﻧﻴﺴﺖ )ﺩﺭ ﺑﺨﺶ ﺑﻌﺪ‬
‫ﺗﻌﺮﻳﻔﻲ ﺑﺮﺍﻱ ﺑﻬﻴﻨﻪ ﺑﻮﺩﻥ ﺗﻌﺎﺩﻝ ﻫﺎ ﺍﺭﺍﺋﻪ ﺧﻮﺍﻫﻴﻢ ﮐﺮﺩ(‪ .‬ﺍﻟﺒﺘﻪ ﺩﺭ ﻋﻤﻞ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺭﺍ ﺑﺎﻳﺪ ﺑﺎ ﻳﮏ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﻣﺪﻝ ﮐﺮﺩ ﺯﻳﺮﺍ ﮐﻪ‬
‫ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺗﻌﺪﺍﺩ ﺯﻳﺎﺩﻱ ﺑﺴﺘﻪ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺧﻮﺍﻫﻨﺪ ﺩﺍﺷﺖ‪.‬‬
‫‪ -2-2‬ﺑﺎﺯﻱ ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻣﺸﺘﺮﮎ ﺑﻪ ﻣﻘﺼﺪ‬
‫ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﻣﺸﺎﺑﻪ ﻣﺴﺎﻟﻪ ﺍﺭﺳﺎﻝ ﻣﺘﻘﺎﺑﻞ ﺩﺍﺩﻩ ﻫﺎﺳﺖ‪ ،‬ﺑﺎ ﺍﻳﻦ ﺗﻔﺎﻭﺕ ﮐﻪ ﺍﻳﻦ ﺑﺎﺭ ﺩﻭ ﮔﺮﻩ ﺷﺒﮑﻪ ﺑﺎﻳﺪ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﺍﺯ ﻳﮏ ﻣﺒﺪﺍ ﺗﺎ ﻳﮏ‬
‫ﻣﻘﺼﺪ ﻣﺸﺘﺮﮎ ﺑﺎ ﻳﮑﺪﻳﮕﺮ ﻫﻤﮑﺎﺭﻱ ﮐﻨﻨﺪ‪.‬‬
‫ﺑﻪ ﻃﻮﺭ ﻣﺸﺎﺑﻪ ﺑﺮﺍﻱ ﻓﺮﻡ ﺍﺳﺘﺮﺍﺗﮋﻳﮏ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺩﺍﺭﻳﻢ‪:‬‬
‫ﺩﺭ ﺍﻳﻨﺠﺎ ﻧﻴﺰ ﺑﻪ ﺭﻭﺵ ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎﻱ ﻏﺎﻟﺐ ﺿﻌﻴﻒ ﻣﻲ ﺗﻮﺍﻥ ﺩﻳﺪ ﮐﻪ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱ ﺯﻭﺝ )‪ (F,F‬ﺍﺳﺖ‪ .‬ﺑﻪ ﻭﺿﻮﺡ ﺩﺭ ﺍﻳﻦ ﻣﺜﺎﻝ ﺗﻌﺎﺩﻝ‬
‫ﺑﺎﺯﻱ ﺑﻬﻴﻨﻪ ﺍﺳﺖ ﻳﻌﻨﻲ ﺳﻮﺩ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺩﺭ ﺗﻌﺎﺩﻝ ﺑﻴﺶ ﺍﺯ ﺳﻮﺩ ﺁﻥ ﻫﺎ ﺑﺎ ﺍﻧﺘﺨﺎﺏ ﻫﺮ ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎﻱ ﺩﻳﮕﺮﻱ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﻣﺜﺎﻝ ﻧﻴﺰ ﻣﺎﻧﻨﺪ‬
‫ﻣﺜﺎﻝ ﻗﺒﻞ ﻣﺮﺑﻮﻁ ﺑﻪ ﻻﻳﻪ ﺷﺒﮑﻪ ﺍﺳﺖ‪.‬‬
‫‪ -3-2‬ﺑﺎﺯﻱ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ‬
‫ﻓﺮﺽ ﮐﻨﻴﺪ ﺩﻭ ﻓﺮﺳﺘﻨﺪﻩ ﺑﺨﻮﺍﻫﻨﺪ ﺑﻪ ﻃﻮﺭ ﻫﻤﺰﻣﺎﻥ ﺍﺯ ﻳﮏ ﮐﺎﻧﺎﻝ ﻣﺨﺎﺑﺮﺍﺗﻲ ﻣﺸﺘﺮﮎ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻫﺎﻱ ﺧﻮﺩ ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻨﺪ‪.‬‬
‫ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺮﻳﮏ ﺍﺯ ﺍﻳﻦ ﺩﻭ ﻓﺮﺳﺘﻨﺪﻩ ﺷﺎﻣﻞ ﺍﺭﺳﺎﻝ )‪ (T‬ﻳﺎ ﺍﻧﺘﻈﺎﺭ )‪ (W‬ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺑﺪﻟﻴﻞ ﺍﻳﺠﺎﺩ ﺗﺪﺍﺧﻞ ﻣﻲ ﺩﺍﻧﻴﻢ ﮐﻪ ﺍﮔﺮ ﻫﺮ ﺩﻭ‬
‫ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﻃﻮﺭ ﻫﻤﺰﻣﺎﻥ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﮐﻨﻨﺪ‪ ،‬ﻫﻴﭽﻴﮏ ﺍﺯ ﺁﻧﻬﺎ ﻣﻮﻓﻖ ﺑﻪ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺧﻮﺩ ﺑﻪ ﻣﻘﺼﺪ ﻧﺨﻮﺍﻫﻨﺪ ﺷﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ‬
‫ﻫﺰﻳﻨﻪ ﺛﺎﺑﺖ ‪ C‬ﺭﺍ ﺑﺮﺍﻱ ﺗﻮﺍﻥ ﻻﺯﻡ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻓﺮﻡ ﺍﺳﺘﺮﺍﺗﮋﻳﮏ ﺑﺎﺯﻱ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
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‫ﺑﻪ ﺭﺍﺣﺘﻲ ﻣﻲ ﺗﻮﺍﻥ ﺩﻳﺪ ﮐﻪ ﺍﻳﻦ ﺑﺎﺯﻱ ﺩﺍﺭﺍﻱ ‪ 2‬ﺗﻌﺎﺩﻝ ﻧﺶ ﺧﺎﻟﺺ ﺍﺳﺖ‪ (W,T) :‬ﻭ )‪ .(T,W‬ﻭﻟﻲ ﻫﻴﭽﻴﮏ ﺍﺯ ﺍﻳﻦ ﺗﻌﺎﺩﻝ ﻫﺎ ﻣﻨﺼﻔﺎﻧﻪ‬
‫ﻧﻴﺴﺘﻨﺪ‪ .‬ﻳﮑﻲ ﺍﺯ ﻓﺎﮐﺘﻮﺭ ﻫﺎﻱ ﻣﻬﻢ ﺑﺮﺍﻱ ﺍﻧﺘﺨﺎﺏ ﺗﻌﺎﺩﻝ ﺑﺮﺍﻱ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﺑﻪ ﻋﻨﻮﺍﻥ ﭘﺮﻭﺗﮑﻞ‪ ،‬ﻣﻨﺼﻔﺎﻧﻪ ﺑﻮﺩﻥ ﺁﻧﻬﺎﺳﺖ‪ .‬ﺧﻮﺷﺒﺨﺘﺎﻧﻪ‬
‫ﺍﻳﻦ ﺑﺎﺯﻱ ﺩﺍﺭﺍﻱ ﻳﮏ ﺗﻌﺎﺩﻝ ﻣﻨﺼﻔﺎﻧﻪ ﻣﺮﮐﺐ ﻧﻴﺰ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﻓﺮﺽ ﮐﻨﻴﺪ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻭﻝ ﻭ ﺩﻭﻡ ﺑﻪ ﺗﺮﺗﻴﺐ ﺑﺎ ﺍﺣﺘﻤﺎﻻﺕ ‪ p1‬ﻭ ‪ p2‬ﺍﻗﺪﺍﻡ ﺑﻪ‬
‫ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻭ ﺑﻪ ﺍﺣﺘﻤﺎﻝ ‪ q1‬ﻭ ‪ q2‬ﻣﻨﺘﻈﺮ ﺑﻤﺎﻧﻨﺪ ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﺗﺎﺑﻊ ﺳﻮﺩ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻭﻝ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
‫ﺑﻪ ﻃﻮﺭ ﻣﺸﺎﺑﻪ ﺩﺍﺭﻳﻢ‪:‬‬
‫)‬
‫‪−‬‬
‫‪(1 −‬‬
‫‪)(1 − ) −‬‬
‫=‬
‫)‬
‫‪−‬‬
‫‪(1 −‬‬
‫‪u = q (1 −‬‬
‫= ‪u‬‬
‫ﺣﺎﻝ ﺑﺪﻳﻬﻲ ﺍﺳﺖ ﮐﻪ ﺯﻭﺝ ﺍﺳﺘﺮﺍﺗﮋﻱ ) ‪ (1 − , 1 −‬ﺗﻌﺎﺩﻝ ﻣﺮﮐﺐ ﺑﺎﺯﻱ ﻓﻮﻕ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﺍﻣﻴﺪ ﺭﻳﺎﺿﻲ ﺳﻮﺩ ﺑﺎﺯﻳﮑﻨﺎﻥ )‪(0.0‬‬
‫ﺍﺳﺖ‪ .‬ﭘﺲ ﺍﻳﻦ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎ ﻭﺟﻮﺩ ﻣﻨﺼﻔﺎﻧﻪ ﺑﻮﺩﻥ‪ ،‬ﺑﻬﻴﻨﻪ ﻧﻴﺴﺖ‪ .‬ﺑﻬﻴﻨﻪ ﺑﻮﺩﻥ ﻧﻘﺎﻁ ﺗﻌﺎﺩﻝ‪ ،‬ﺩﻳﮕﺮ ﻋﺎﻣﻞ ﻣﻬﻢ ﺩﺭ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ‬
‫ﺷﺒﮑﻪ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﺑﺎﺯﻱ ﺑﺮ ﺧﻼﻑ ﺩﻭ ﺑﺎﺯﻱ ﻗﺒﻞ‪ ،‬ﻣﺮﺑﻮﻁ ﺑﻪ ﻻﻳﻪ ﮐﻨﺘﺮﻝ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﻣﺤﻴﻂ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺑﺮﺭﺳﻲ ﺣﺎﻟﺖ ﮐﻠﻲ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺑﺎ ‪n‬‬
‫ﺑﺎﺯﻳﮑﻦ ﺩﺭ ﻳﮏ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺭﺍ ﺑﻪ ﺑﺨﺶ ﺑﻌﺪ ﻣﻮﮐﻮﻝ ﻣﻲ ﮐﻨﻴﻢ‪.‬‬
‫‪ -4-2‬ﺑﺎﺯﻱ ﺍﻳﺠﺎﺩ ﺍﺧﺘﻼﻝ ﺩﺭ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ‬
‫ﻓﺮﺽ ﮐﻨﻴﺪ ﮐﻪ ﻳﮏ ﻓﺮﺳﺘﻨﺪﻩ ﺍﺧﻼﻝ ﮔﺮ ﻣﻲ ﺧﻮﺍﻫﺪ ﺍﺯ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻳﮏ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﻣﻘﺼﺪ ﺟﻠﻮﮔﻴﺮﻱ ﮐﻨﺪ‪ .‬ﺍﻳﻦ ﻓﺮﺳﺘﻨﺪﻩ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﻪ‬
‫ﺩﻟﺨﻮﺍﻩ ﻳﮑﻲ ﺍﺯ ﺩﻭ ﮐﺎﻧﺎﻝ ‪ A‬ﻳﺎ ‪ B‬ﺭﺍ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺧﻮﺩ ﺍﻧﺘﺨﺎﺏ ﮐﻨﺪ‪ .‬ﺑﻪ ﻃﻮﺭ ﻣﺸﺎﺑﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺍﺧﻼﻝ ﮔﺮ ﻳﮑﻲ ﺍﺯ ﺍﻳﻦ ﺩﻭ ﮐﺎﻧﺎﻝ ﺭﺍ‬
‫ﺍﻧﺘﺨﺎﺏ ﻭ ﺩﺭ ﺁﻥ ﺍﻏﺘﺸﺎﺵ ﺍﻳﺠﺎﺩ ﮐﻨﺪ‪ .‬ﺣﺎﻝ ﺍﮔﺮ ﺍﺧﻼﻝ ﮔﺮ ﺗﻮﺍﻧﺴﺘﻪ ﺑﺎﺷﺪ ﮐﺎﻧﺎﻝ ﻓﺮﺳﺘﻨﺪﻩ ﺭﺍ ﺑﻪ ﺩﺭﺳﺘﻲ ﺗﺸﺨﻴﺺ ﺩﻫﺪ‪ ،‬ﻓﺮﺳﺘﻨﺪﻩ ﻗﺎﺩﺭ ﺑﻪ‬
‫ﺍﺭﺳﺎﻝ ﭘﻴﺎﻡ ﺧﻮﺩ ﻧﺨﻮﺍﻫﺪ ﺑﻮﺩ ﻭ ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﺍﺧﻼﻝ ﮔﺮ ﻭ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﺗﺮﺗﻴﺐ ﺳﻮﺩ ‪ +1‬ﻭ ‪ -1‬ﺭﺍ ﺧﻮﺍﻫﻨﺪ ﺩﺍﺷﺖ ﻭ ﺩﺭ ﻏﻴﺮ ﺍﻳﻦ ﺻﻮﺭﺕ‬
‫ﺳﻮﺩ ﺁﻧﻬﺎ ﺑﻪ ﺗﺮﺗﻴﺐ ‪ -1‬ﻭ ‪ +1‬ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﭘﺲ ﻓﺮﻡ ﺍﺳﺘﺮﺍﺗﮋﻳﮏ ﺑﺎﺯﻱ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
‫ﺍﻳﻦ ﺑﺎﺯﻱ ﻧﻤﻮﻧﻪ ﺍﻱ ﺍﺯ ﺑﺎﺯﻱ ﻫﺎﻱ ﺑﺎ ﻣﺠﻤﻮﻉ ﺳﻮﺩ ﺻﻔﺮ ﺍﺳﺖ‪ .‬ﺑﻪ ﺭﺍﺣﺘﻲ ﻣﻲ ﺗﻮﺍﻥ ﺩﻳﺪ ﮐﻪ ﺍﻳﻦ ﺑﺎﺯﻱ ﺗﻌﺎﺩﻝ ﺧﺎﻟﺺ ﻧﺪﺍﺭﺩ‪ .‬ﻭﻟﻲ ﺍﺯ ﺁﻧﺠﺎ ﮐﻪ‬
‫ﻗﻀﻴﻪ ﻧﺶ ﻭﺟﻮﺩ ﺣﺪﺍﻗﻞ ﻳﮏ ﺗﻌﺎﺩﻝ ﺭﺍ ﺑﺮﺍﻱ ﺍﻳﻦ ﺑﺎﺯﻱ ﺗﻀﻤﻴﻦ ﻣﻲ ﮐﻨﺪ‪ ،‬ﺑﺎﻳﺪ ﺑﻪ ﺩﻧﺒﺎﻝ ﺗﻌﺎﺩﻝ ﻣﺮﮐﺐ ﺑﺮﺍﻱ ﺍﻳﻦ ﺑﺎﺯﻱ ﺑﺎﺷﻴﻢ‪ .‬ﺍﺯ ﺗﻘﺎﺭﻥ‬
‫ﺑﺎﺯﻱ ﺍﻧﺘﻈﺎﺭ ﺩﺍﺭﻳﻢ ﺯﻭﺝ ﺍﺳﺘﺮﺍﺗﮋﻱ )‪(−1/2 ,1/2‬ﻳﮏ ﺗﻌﺎﺩﻝ ﺑﺮﺍﻱ ﺍﻳﻦ ﺑﺎﺯﻱ ﺑﺎﺷﺪ‪ .‬ﺩﺭ ﺣﻘﻴﻘﺖ ﻣﻲ ﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﮐﻪ ﺍﻳﻦ ﺯﻭﺝ ﺗﻨﻬﺎ‬
‫ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﻓﻮﻕ ﺍﺳﺖ‪.‬‬
‫ﺍﻳﻦ ﺑﺎﺯﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﭘﺎﻳﻴﻦ ﺗﺮﻳﻦ ﻻﻳﻪ ﺷﺒﮑﻪ ﻳﻌﻨﻲ ﻻﻳﻪ ﻓﻴﺰﻳﮑﻲ ﺍﺳﺖ‪ .‬ﺩﺭ ﺑﺨﺶ ﺁﺧﺮ ﺍﻳﻦ ﺑﺎﺯﻱ ﺭﺍ ﺑﻪ ﺗﻔﻀﻴﻞ ﻭ ﺑﺎ ﻧﮕﺎﻩ ﺍﺯ ﺩﻳﺪ ﺗﺌﻮﺭﻱ‬
‫ﺍﻃﻼﻋﺎﺕ ﺑﺮﺭﺳﻲ ﺧﻮﺍﻫﻴﻢ ﮐﺮﺩ‬
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‫‪ -3‬ﺻﺤﺖ ﻓﺮﺿﻴﺎﺕ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ‬
‫‪ -1-3‬ﻓﺮﺽ ﻋﻘﻼﻧﻴﺖ‬
‫ﻳﮑﻲ ﺍﺯ ﺍﻧﺘﻘﺎﺩ ﻫﺎﻳﻲ ﮐﻪ ﺑﻪ ﮐﺎﺭﺑﺮﺩ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺩﺭ ﻣﺪﻝ ﮐﺮﺩﻥ ﻭ ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﺍﻧﺴﺎﻥ ﻫﺎ ﻭﺍﺭﺩ ﺍﺳﺖ ‪ ،‬ﺻﺤﺖ ﻓﺮﺽ ﻋﻘﻼﻧﻴﺖ ﺩﺭ ﻣﻮﺭﺩ‬
‫ﺍﻓﺮﺍﺩ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻧﺪﻩ ﻳﺎ ﻫﻤﺎﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺳﺖ‪ .‬ﻳﻌﻨﻲ ﺁﻳﺎ ﺍﻧﺴﺎﻥ ﻫﺎ ﻫﻤﻮﺍﺭﻩ ﺑﻬﺘﺮﻳﻦ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﻮﺩ ﺭﺍ ﺑﺎ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺗﻤﺎﻡ ﺍﺳﺘﺮﺍﺗﮋﻱ‬
‫ﻫﺎﻱ ﻣﻤﮑﻦ ﺑﺮﺍﻱ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺣﺪﺍﮐﺜﺮ ﻧﻤﻮﺩﻥ ﺳﻮﺩ ﺧﻮﺩ ﺍﻧﺘﺨﺎﺏ ﻣﻴﮑﻨﻨﺪ؟‬
‫ﺁﻧﭽﻪ ﻣﺴﻠﻢ ﺍﺳﺖ ﺍﻳﻨﮑﻪ ﻣﺪﻝ ﮐﺮﺩﻥ ﻓﺮﺍﻳﻨﺪ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﺍﻧﺴﺎﻥ ﻫﺎ ﺑﺎ ﺗﻌﺪﺍﺩ ﻣﺤﺪﻭﺩﻱ ﭘﺎﺭﺍﻣﺘﺮ ﻭ ﻣﻌﺎﺩﻟﻪ ﻧﻤﻴﺘﻮﺍﻧﺪ ﮐﺎﻣﻼﹰ ﺻﺤﻴﺢ ﺑﺎﺷﺪ‪.‬‬
‫ﻭﻟﻲ ﺧﻮﺷﺒﺨﺘﺎﻧﻪ ﺍﻳﻦ ﻓﺮﺽ ﺩﺭ ﻣﻮﺭﺩ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻧﺪﻩ ﻫﺎ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﺗﺎ ﺣﺪ ﺧﻮﺑﻲ ﺑﺮﻗﺮﺍﺭ ﺍﺳﺖ ﺯﻳﺮﺍ ﺗﺠﻬﻴﺰﺍﺕ ﺷﺒﮑﻪ ﻫﺎ ﻳﮏ ﺑﺎﺭ ﻭ‬
‫ﻳﺎ ﺑﺎ ﻓﻮﺍﺻﻞ ﻃﻮﻻﻧﻲ ﺑﺮﻧﺎﻣﻪ ﺭﻳﺰﻱ ﻣﻲ ﺷﻮﻧﺪ ﺗﺎ ﺍﺯ ﭘﺮﻭﺗﮑﻞ ﻭ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﺎﺹ ﺩﺭ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﻫﺎ ﭘﻴﺮﻭﻱ ﮐﻨﻨﺪ ﻭ ﻣﺴﻠﻤﺎﹰ ﻣﺪﻝ ﺳﺎﺯﻱ‬
‫ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﻣﺎﺷﻴﻦ ﻫﺎ ﺑﺴﻴﺎﺭ ﺳﺎﺩﻩ ﺗﺮ ﺍﺯ ﻣﺪﻝ ﺳﺎﺯﻱ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﺍﻧﺴﺎﻥ ﻫﺎ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬
‫‪ -2-3‬ﻓﺮﺽ ﺍﻃﻼﻋﺎﺕ ﮐﺎﻣﻞ‬
‫ﺗﻤﺎﻡ ﻣﻘﺎﻟﻪ ﻫﺎﻳﻲ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﺤﺚ ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﺍﺯ ﻧﻮﻉ ﺑﺎﺯﻱ ﻫﺎﻱ ﺑﺎ ﺍﻃﻼﻋﺎﺕ ﮐﺎﻣﻞ ﺑﻮﺩﻧﺪ‪ .‬ﻳﻌﻨﻲ ﺩﺭ ﺁﻥ ﻫﺎ ﻓﺮﺽ ﮐﺮﺩﻳﻢ ﮐﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ‬
‫ﺍﺯ ﻫﻮﻳﺖ ﻳﮑﺪﻳﮕﺮ ‪ ،‬ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎﻱ ﻣﻤﮑﻦ ﺑﺮﺍﻱ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺩﻳﮕﺮ ﻭ ﺗﻮﺍﺑﻊ ﺳﻮﺩ ﺁﻥ ﻫﺎ ﺍﻃﻼﻉ ﺩﺍﺭﻧﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻓﺮﺽ ﮐﺮﺩﻳﻢ ﮐﻪ ﺩﺭ ﺑﺎﺯﻳﻬﺎﻱ‬
‫ﭘﻲ ﺩﺭ ﭘﻲ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺍﺯ ﺭﻓﺘﺎﺭ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺗﻤﺎﻣﻲ ﻣﺮﺍﺣﻞ ﻗﺒﻠﻲ ﺑﻪ ﻃﻮﺭ ﮐﺎﻣﻞ ﺍﻃﻼﻉ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﺍﻣ‪‬ﺎ ﺍﻳﻦ ﻓﺮﺽ ﺩﺭ ﺍﻳﻦ ﻣﻮﺭﺩ‬
‫ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﺩﺭ ﻣﻮﺍﺭﺩ ﺯﻳﺎﺩﻱ ﺑﺎ ﺍﺷﮑﺎﻝ ﺭﻭﺑﺮﻭ ﺍﺳﺖ ﻭ ﺩﺭ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎ ﺑﺮ ﭘﺎﻱۀ ﺍﻳﻦ ﻓﺮﺽ ﺑﺎﻳﺪ ﮐﻤﻲ ﺍﺣﺘﻴﺎﻁ ﮐﺮﺩ‪.‬‬
‫ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺑﺎﺯﻱ ﻫﻤﺎﻥ ﺍﺭﺳﺎﻝ ﻣﻘﺎﺑﻠﻪ ﺑﺴﺘﻪ ﻫﺎﻱ ﺍﻃﻼﻋﺎﺕ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﺮﻳﺪ‪ .‬ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﻣﻲ ﺩﺍﻧﻴﺪ ﺩﺭ ﮐﺎﻧﺎﻝ ﻫﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ ﻭ ﺑﻪ‬
‫ﺧﺼﻮﺹ ﮐﺎﻧﺎﻝ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﺑﻪ ﺩﻻﻳﻞ ﻣﺘﻌﺪﺩ ﻫﻤﻮﺍﺭﻩ ﺍﻣﮑﺎﻥ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺑﺎ ﺧﻄﺎ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪.‬ﺣﺎﻝ ﻓﺮﺽ ﮐﻨﻴﺪ ﮐﻪ ﺩﺭ ﺁﻥ ﻣﺜﺎﻝ ﻫﺮ ﺩﻭ‬
‫ﻓﺮﺳﺘﻨﺪﻩ ﺩﺭ ﺣﺎﻝ ﻫﻤﮑﺎﺭﻱ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﻣﺘﻘﺎﺑﻞ ﺑﺴﺘﻪ ﻫﺎﻱ ﺍﻃﻼﻋﺎﺕ ﻳﮑﺪﻳﮕﺮ ﺑﺎﺷﻨﺪ ﻭﻟﻲ ﺩﺭ ﻳﮏ ﻟﺤﻈﻪ ﻭﺿﻌﻴﺖ ﮐﺎﻧﺎﻝ ﺭﺍﺩﻳﻮﻳﻲ ﺍﺯ‬
‫ﻓﺮﺳﺘﻨﺪﻩ ﺍﻭﻝ ﺗﺎ ﺍﻳﺴﺘﮕﺎﻩ ﮔﻴﺮﻧﺪﻩ ﻣﺮﺑﻮﻁ ﺑﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺩﻭﻡ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺗﻐﻴﻴﺮ ﮐﻨﺪ ﮐﻪ ﺑﺴﺘﻪ ﻫﺎﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺩﻭﻡ ﺑﻪ ﻣﻘﺼﺪ ﻧﺮﺳﺪ‪.‬‬
‫ﺩﺭ ﺍﻳﻦ ﻟﺤﻈﻪ ﻣﻤﮑﻦ ﺍﺳﺖ ﻓﺮﺳﺘﻨﺪﻩ ﺩﻭﻡ ﺑﻪ ﻏﻠﻂ ﺗﺼﻮﺭ ﮐﻨﺪ ﮐﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻭﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺍﻭ ﺭﺍ ﺑﻪ ﻣﻘﺼﺪ ﻫﺪﺍﻳﺖ ﻧﻤﻲ ﮐﻨﺪ ﻭ ﺗﺼﻤﻴﻢ‬
‫ﻋﺪﻡ ﻫﺪﺍﻳﺖ ﺑﺴﺘﻪ ﻫﺎﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻭﻝ ﮐﻨﺪ ﮐﻪ ﺍﻳﻦ ﺗﺼﻤﻴﻢ ﮔﻴﺮﻱ ﻫﺎ ﻣﻤﮑﻦ ﺍﺳﺖ ﺩﺭ ﻧﻬﺎﻳﺖ ﺑﻪ ﺗﺨﺮﻳﺐ ﮐﺎﻣﻞ ﻫﺮ ﺩﻭ ﻟﻴﻨﮏ‬
‫ﺷﺒﮑﻪ ﺷﻮﺩ‪.‬‬
‫ﭘﺲ ﻫﻤﻮﺍﺭﻩ ﺩﺭ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﻣﺮﺑﻮﻁ ﺑﻪ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﺑﺎﻳﺪ ﺻﺤﺖ ﺍﻃﻼﻋﺎﺕ ﺍﻱ ﮐﻪ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺩﺍﺭﺩ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ‬
‫ﮔﻴﺮﻳﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻓﺮﺽ ﺍﻃﻼﻋﺎﺕ ﮐﺎﻣﻞ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺯ ﺗﺎﺑﻊ ﺳﻮﺩ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻧﻴﺰ ﺑﺎ ﺍﺷﮑﺎﻻﺗﻲ ﺭﻭﺑﺮﻭﺳﺖ‪ .‬ﻳﮑﻲ ﺍﺯ ﺍﻳﻦ ﺍﺷﮑﺎﻻﺕ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ‬
‫ﺩﺭ ﻫﻤﺎﻥ ﻣﺜﺎﻝ ﺍﺭﺳﺎﻝ ﻣﺘﻘﺎﺑﻞ ﺑﺴﺘﻪ ﻫﺎ ﺩﺭ ﺷﺒﮑﻪ ﻣﺸﺎﻫﺪﻩ ﮐﺮﺩ‪ .‬ﺩﺭ ﺁﻧﺠﺎ ﻓﺮﺽ ﮐﺮﺩﻳﻢ ﮐﻪ ﺍﺭﺳﺎﻝ ﺻﺤﻴﺢ ﻫﺮ ﺑﺴﺘﻪ ﺑﺮﺍﻱ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ‬
‫ﻣﻘﺪﺍﺭ ﺛﺎﺑﺖ ‪ 1‬ﻭﺍﺣﺪ ﺍﺭﺯﺵ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ ﻭﻟﻲ ﺍﻳﻦ ﻓﺮﺽ ﮐﺎﻣﻼ ﺩﺭﺳﺖ ﻧﻴﺴﺖ ﻭ ﺩﺭ ﺣﺎﻟﺖ ﮐﻠﻲ ﺍﺭﺯﺵ ﻫﺮ ﺑﺴﺘﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺩﺭ ﻣﻮﻗﻌﻴﺖ ﻫﺎﻱ‬
‫ﻣﺨﺘﻠﻒ ﻣﺘﻔﺎﻭﺕ ﺑﺎﺷﺪ‪ .‬ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎ ﻣﻤﮑﻦ ﺍﺳﺖ ﺣﺎﻭﻱ ﺍﻃﻼﻋﺎﺕ ﺑﺴﻴﺎﺭ ﺑﺎﺍﺭﺯﺷﻲ ﺑﺎﺷﻨﺪ ﻭ ﻳﺎ ﺍﻳﻨﮑﻪ ﺍﺭﺯﺵ ﺁﻧﻬﺎ ﺑﻪ ﺍﻧﺪﺍﺯﻩ‬
‫ﺍﻱ ﮐﻢ ﺑﺎﺷﺪ ﮐﻪ ﺍﺭﺳﺎﻝ ﻧﺸﺪﻥ ﺁﻧﻬﺎ ﺍﺷﮑﺎﻟﻲ ﺩﺭ ﺍﺩﺍﻣﻪ ﺍﺭﺗﺒﺎﻁ ﺑﻪ ﻭﺟﻮﺩ ﻧﻴﺎﻭﺭﺩ‪.‬‬
‫ﺑﻨﺎﺑﺮﺍﻳﻦ ﺍﻃﻼﻋﺎﺕ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺎ ﻭ ﺑﺨﺼﻮﺹ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﻧﺎﻗﺺ ﻭ ﻳﺎ ﺣﺘﻲ ﻧﺎﺩﺭﺳﺖ ﺑﺎﺷﻨﺪ‪ .‬ﮐﺎﺭﺑﺮﺩ ﻧﻈﺮﻳﻪ‬
‫ﺑﺎﺯﻱ ﻫﺎﻱ ﺑﺎ ﺍﻃﻼﻋﺎﺕ ﻏﻴﺮﮐﺎﻣﻞ ﺩﺭ ﻣﺪﻝ ﺳﺎﺯﻱ ﺷﺒﮑﻪ ﻫﺎ ﺑﻪ ﺗﺎﺯﮔﻲ ﺩﺭﭼﻨﺪ ﻣﻘﺎﻟﻪ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﺳﺖ‪.‬‬
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‫‪ -3-3‬ﻓﺮﺽ ﻧﺎﻣﺘﻨﺎﻫﻲ ﺑﻮﺩﻥ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﻫﺎ‬
‫ﺩﺭ ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﻫﺎ ﻣﺎﻧﻨﺪ ﺑﺎﺯﻱ ﻫﺎﻱ ﺩﺳﺘﺮﺳﻲ ﭼﻨﺪﮔﺎﻧﻪ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ﻭ ﻳﺎ ﺑﺎﺯﻱ ﮐﻨﺘﺮﻝ ﺗﻮﺍﻥ ﺑﻪ ﻃﻮﺭ ﺿﻤﻨﻲ‬
‫ﻓﺮﺽ ﮐﺮﺩﻳﻢ ﮐﻪ ﺑﺎﺯﻱ ﻧﺎﻣﺘﻨﺎﻫﻲ ﺑﺎﺷﺪ ﻳﻌﻨﻲ ﻫﻴﭽﻴﮏ ﺍﺯ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻃﻼﻋﻲ ﺍﺯ ﺯﻣﺎﻥ ﭘﺎﻳﺎﻥ ﺁﻥ ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ‪ .‬ﺑﺪﻭﻥ ﺍﻳﻦ ﻓﺮﺽ ﺭﺍﻩ ﺣﻞ‬
‫ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺑﻪ ﻃﻮﺭ ﮐﻠﻲ ﺍﺷﺘﺒﺎﻩ ﺧﻮﺍﻫﺪ ﺑﻮﺩ ﻭ ﺑﺮﺍﻱ ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻫﺎﻱ ﻣﺘﻨﺎﻫﻲ ﺍﺻﻮﻻ ﺑﺎﻳﺪ ﺭﻭﺵ ﻫﺎﻱ ﺩﻳﮕﺮﻱ ﺭﺍ ﺁﺯﻣﻮﺩ )ﻣﺎﻧﻨﺪ ﺭﻭﺵ‬
‫ﺍﺳﺘﻘﺮﺍﻳﻲ ﺍﺯ ﻣﺮﺣﻠﻪ ﺁﺧﺮ ﺑﻪ ﺍﻭﻝ(‪.‬‬
‫ﻣﻲ ﺩﺍﻧﻴﻢ ﺩﺭ ﺑﺴﻴﺎﺭﻱ ﺍﺯ ﻣﻮﺍﺭﺩ ﺗﺠﻬﻴﺰﺍﺕ ﺷﺒﮑﻪ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺗﺨﻤﻴﻦ ﺧﻮﺑﻲ ﺍﺯ ﺯﻣﺎﻥ ﭘﺎﻳﺎﻥ ﻳﺎﻓﺘﻦ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﺩﺍﺷﺘﻪ‬
‫ﺑﺎﺷﻨﺪ‪ .‬ﻣﺜﻼ ﻣﻤﮑﻦ ﺍﺳﺖ ﻳﮑﻲ ﺍﺯ ﮐﺎﺭﺑﺮﺍﻥ ﺷﺒﮑﻪ ﺑﺪﺍﻧﺪ ﮐﻪ ﺍﺭﺳﺎﻝ ﺍﻃﻼﻋﺎﺗﺶ ﭼﻪ ﺯﻣﺎﻧﻲ ﺑﻪ ﭘﺎﻳﺎﻥ ﺧﻮﺍﻫﺪ ﺭﺳﻴﺪ ﻭ ﻳﺎ ﺑﺪﺍﻧﺪ ﮐﻪ ﭼﻪ ﺯﻣﺎﻧﻲ ﺍﺯ‬
‫ﺷﺒﮑﻪ ﺧﺎﺭﺝ ﺧﻮﺍﻫﺪ ﺷﺪ )ﺑﻪ ﺩﻻﻳﻠﻲ ﻣﺎﻧﻨﺪ ﺟﺎﺑﺠﺎﻳﻲ ﻭ ﻳﺎ ﺍﺗﻤﺎﻡ ﺗﻮﺍﻥ(‪.‬‬
‫ﺩﺭ ﺍﺑﺘﺪﺍ ﻣﻤﮑﻦ ﺍﺳﺖ ﺍﻳﻦ ﻃﻮﺭ ﺑﻪ ﻧﻈﺮ ﺑﺮﺳﺪ ﮐﻪ ﺍﻳﻦ ﻣﻄﻠﺐ ﺻﺤﺖ ﻓﺮﺿﻴﺎﺕ ﺍﻧﺠﺎﻡ ﮔﺮﻓﺘﻪ ﺭﺍ ﺯﻳﺮ ﺳﻮﺍﻝ ﻣﻲ ﺑﺮﺩ ﻭﻟﻲ ﺑﺎﻳﺪ ﺩﻗﺖ ﺩﺍﺷﺖ ﮐﻪ‬
‫ﺗﻤﺎﻡ ﺍﻃﻼﻋﺎﺕ ﻓﻮﻕ ﺍﻟﺬﮐﺮ ﺍﺯ ﺯﻣﺎﻥ ﺍﺗﻤﺎﻡ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻫﺎ ﻣﺮﺑﻮﻁ ﺑﻪ ﻻﻳﻪ ﻫﺎﻱ ﺑﺎﻻﻱ ﺷﺒﮑﻪ ﻳﻌﻨﻲ ﻻﻳﻪ ﮐﺎﺭﺑﺮﺩﻱ ﺍﺳﺖ‪ ،‬ﺩﺭ ﺻﻮﺭﺗﻲ ﮐﻪ ﺑﺎﺯﻱ‬
‫ﻫﺎﻱ ﻣﻮﺭﺩ ﺑﺤﺚ ﻣﺎ ﺩﺭ ﻻﻳﻪ ﻫﺎﻱ ﭘﺎﻳﻴﻦ ﺷﺒﮑﻪ ﺍﻧﺠﺎﻡ ﻣﻲ ﭘﺬﻳﺮﻧﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﻓﺮﺽ ﻧﺎﻣﺘﻨﺎﻫﻲ ﺑﻮﺩﻥ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﻓﺮﺿﻲ ﻗﺎﺑﻞ‬
‫ﻗﺒﻮﻝ ﺍﺳﺖ‪.‬‬
‫‪ -4-3‬ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﺩﺭ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ‬
‫ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﮔﻔﺘﻪ ﺷﺪ ﺩﺭ ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ ﻫﺎ ﺿﺮﻳﺒﻲ ﮐﻤﺘﺮ ﺍﺯ ﻳﮏ ﺑﻪ ﻋﻨﻮﺍﻥ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﻲ‬
‫ﺷﻮﺩ ﮐﻪ ﺗﺎﺑﻊ ﺳﻮﺩ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﻧﺴﺒﺖ ﺑﻪ ﻣﺮﺣﻠﻪ ﻗﺒﻞ ﺩﺭ ﺁﻥ ﺿﺮﺏ ﻣﻲ ﺷﻮﺩ‪ .‬ﺗﻮﺟﻴﻪ ﻭﺟﻮﺩ ﺍﻳﻦ ﺿﺮﻳﺐ ﺩﺭ ﻣﺴﺎﺋﻞ ﺍﻗﺘﺼﺎﺩﻱ‬
‫ﺳﺎﺩﻩ ﺍﺳﺖ‪ :‬ﺑﺪﻟﻴﻞ ﺗﻮﺭﻡ‪ ،‬ﺍﺭﺯﺵ ﻣﻘﺪﺍﺭ ﻣﻌﻴﻨﻲ ﭘﻮﻝ ﺩﺭ ﻫﺮ ﺭﻭﺯ ﻧﺴﺒﺖ ﺑﻪ ﺭﻭﺯ ﻗﺒﻞ ﮐﺎﺳﺘﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﻭﻟﻲ ﺁﻳﺎ ﻓﺮﺽ ﻭﺟﻮﺩ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ‬
‫ﺩﺭ ﻣﻮﺭﺩ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺎ ﻧﻴﺰ ﻣﻮﺟﻪ ﺍﺳﺖ؟‬
‫ﺩﺭ ﻣﻮﺭﺩ ﺷﺒﮑﻪ ﻫﺎ ﻧﻴﺰ ﻣﻲ ﺗﻮﺍﻥ ﺍﺳﺘﺪﻻﻝ ﻣﺸﺎﺑﻬﻲ ﺩﺍﺷﺖ‪ :‬ﻫﺮﻳﮏ ﺍﺯ ﮐﺎﺭﺑﺮﺍﻥ ﺷﺒﮑﻪ ﻣﺎﻳﻠﻨﺪ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﺭﺍ ﻫﺮﭼﻪ ﺳﺮﻳﻌﺘﺮ ﻭ ﺑﺎ‬
‫ﺗﺎﺧﻴﺮ ﮐﻤﺘﺮ ﺑﻪ ﻣﻘﺼﺪ ﺍﺭﺳﺎﻝ ﮐﻨﻨﺪ‪ .‬ﺩﻗﺖ ﮐﻨﻴﺪ ﮐﻪ ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﺩﺭ ﻣﻮﺭﺩ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﺑﺎﺭﺯﺗﺮ ﺍﺳﺖ‪ ،‬ﺯﻳﺮﺍ ﺩﺭﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎ ﺍﺣﺘﻤﺎﻝ‬
‫ﻗﻄﻊ ﻟﻴﻨﮏ ﻫﺎﻱ ﺷﺒﮑﻪ ﻭﺍﺯ ﺑﻴﻦ ﺭﻓﺘﻦ ﺍﺗﺼﺎﻝ ﺑﺎ ﻣﻘﺼﺪ ﺑﺴﻴﺎﺭ ﺑﻴﺸﺘﺮﺍﺳﺖ‪ .‬ﻳﮑﻲ ﺍﺯ ﻣﻬﻤﺘﺮﻳﻦ ﺩﻻﻳﻞ ﺍﻳﻦ ﻣﻮﺿﻮﻉ‪ ،‬ﻗﺎﺑﻠﻴﺖ ﺗﺤﺮﮎ ﮔﺮﻩ ﻫﺎ ﺑﻪ‬
‫ﻋﻨﻮﺍﻥ ﻳﮑﻲ ﺍﺯ ﻭﻳﮋﮔﻲ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬
‫‪ -5-3‬ﻓﺮﺽ ﺧﻮﺩ ﺧﻮﺍﻫﻲ‬
‫ﺩﻗﺖ ﮐﻨﻴﺪ ﮐﻪ ﺩﺭ ﺗﻤﺎﻡ ﻣﺜﺎﻝ ﻫﺎﻱ ﻣﻮﺭﺩ ﺑﺤﺚ ﺧﻮﺩ‪ ،‬ﻓﺮﺽ ﮐﺮﺩﻳﻢ ﮐﻪ ﮐﺎﺭﺑﺮﺍﻥ ﺷﺒﮑﻪ ﺑﺨﻮﺍﻫﻨﺪ ﺳﻮﺩ ﺧﻮﺩ ﺭﺍ ﺑﺪﻭﻥ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺳﻮﺩ‬
‫ﺩﻳﮕﺮﺍﻥ ﺣﺪﺍﮐﺜﺮ ﮐﻨﻨﺪ‪ .‬ﺭﻭﺵ ﻫﺎﻱ ﺍﺳﺘﺪﻻﻝ ﻫﻢ ﻫﻤﮕﻲ ﺑﺮ ﭘﺎﻳﻪ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎﻱ ﻏﻴﺮ ﺗﻌﺎﻭﻧﻲ ﺑﻮﺩ‪ .‬ﻭﻟﻲ ﺩﺭ ﻣﻮﺍﺭﺩﻱ ﮐﺎﺭﺑﺮﺍﻥ ﺷﺒﮑﻪ‬
‫ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﻮﺩ ﺭﺍ ﺑﺮ ﭘﺎﻳﻪ ﺗﻮﺍﻓﻘﺎﺕ ﻗﺒﻠﻲ ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﮐﻨﻨﺪ ﻭ ﻳﺎ ﺑﺎ ﺍﻳﺠﺎﺩ ﺍﺋﺘﻼﻑ‪ ،‬ﺗﻮﺍﺑﻊ ﺳﻮﺩ ﮔﺮﻭﻫﻲ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻧﺪ‪ .‬ﺑﺮﺭﺳﻲ ﺍﻳﻦ‬
‫ﻣﻮﺍﺭﺩ ﺩﺭ ﺣﻴﻄﻪ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎﻱ ﺗﻌﺎﻭﻧﻲ ﺍﺳﺖ‪ .‬ﺑﻪ ﺩﻟﻴﻞ ﭘﻴﭽﻴﺪﮔﻲ ﺑﻴﺸﺘﺮ‪ ،‬ﺑﺮﺭﺳﻲ ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﮐﻤﺘﺮ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﻣﺤﻘﻘﺎﻥ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ‬
‫ﺍﺳﺖ‪.‬‬
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‫‪ -4‬ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺷﺒﮑﻪ‬
‫‪ -1-4‬ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ‬
‫ﺩﺭ ﺍﻳﻦ ﺑﺨﺶ ﻣﻴﺨﻮﺍﻫﻴﻢ ﺑﺎﺯﻱ ﺩﺳﺘﺮﺳﻲ ﺑﻪ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ﺭﺍ ﮐﻪ ﻗﺒﻼ ﻓﻘﻂ ﺑﺎ ‪ 2‬ﺑﺎﺯﻳﮑﻦ ﻭ ﺩﺭ ﻳﮏ ﻣﺮﺣﻠﻪ ﺑﺮﺭﺳﻲ ﮐﺮﺩﻳﻢ ﺭﺍ ﺗﻌﻤﻴﻢ‬
‫ﺩﺍﺩﻩ ﻭ ﺷﺮﺍﻳﻂ ﺁﻥ ﺭﺍ ﺑﻪ ﻭﺍﻗﻌﻴﺖ ﻧﺰﺩﻳﮏ ﺗﺮ ﮐﻨﻴﻢ‪ .‬ﻓﺮﺽ ﮐﻨﻴﺪ ﺗﻌﺪﺍﺩ ‪ n‬ﻓﺮﺳﺘﻨﺪﻩ ﺑﻲ ﺳﻴﻢ ﺑﺨﻮﺍﻫﻨﺪ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﺭﺍ ﺍﺯ‬
‫ﻃﺮﻳﻖ ﻳﮏ ﮐﺎﻧﺎﻝ ﺭﺍﺩﻳﻮﻳﻲ ﻣﺸﺘﺮﮎ ﺑﻪ ﻣﻘﺼﺪ ﺍﺭﺳﺎﻝ ﮐﻨﻨﺪ‪ .‬ﺑﺮﺍﻱ ﺳﺎﺩﮔﻲ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﻫﺮ ﻓﺮﺳﺘﻨﺪﻩ ﺗﻨﻬﺎ ﻳﮏ ﺑﺴﺘﻪ ﺩﺍﺩﻩ‬
‫ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ ﮐﻪ ﭘﺲ ﺍﺯ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﺍﻳﻦ ﺑﺴﺘﻪ ﺍﺯ ﺑﺎﺯﻱ ﺧﺎﺭﺝ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﻫﻤﭽﻨﻴﻦ ﻓﺮﺽ ﮐﻨﻴﺪ ﮐﻪ ﻓﺮﺳﺘﺪﻩ ﻫﺎ ﺍﺯ ﭘﺮﻭﺗﮑﻞ ‪ slotted Aloha‬ﺩﺭ ﺍﺭﺳﺎﻝ ﭘﻴﻐﺎﻡ ﻫﺎﻱ ﺧﻮﺩ ﭘﻴﺮﻭﻱ ﮐﻨﻨﺪ ﻳﻌﻨﻲ ﺯﻣﺎﻥ ﺑﻪ ﺑﺎﺯﻩ‬
‫ﻫﺎﻱ ﮐﻮﭼﮑﻲ ﺗﻘﺴﻴﻢ ﺷﺪﻩ ﺑﺎﺷﺪ ﮐﻪ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺩﺭ ﺍﺑﺘﺪﺍﻱ ﺁﻥ ﺑﺎﺯﻩ ﺯﻣﺎﻧﻲ ﺗﺼﻤﻴﻢ ﺑﻪ ﺍﺭﺳﺎﻝ ﻭ ﻳﺎ ﻋﺪﻡ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺧﻮﺩ‬
‫ﺩﺭ ﺁﻥ ﺑﺎﺯﻩ ﺑﮕﻴﺮﻧﺪ‪ .‬ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻣﺎﻳﻠﻨﺪ ﺩﺍﺩﻩ ﺧﻮﺩ ﺭﺍ ﻫﺮﭼﻪ ﺳﺮﻳﻌﺘﺮ ﺑﻪ ﻣﻘﺼﺪ ﺍﺭﺳﺎﻝ ﮐﻨﻨﺪ ﻭﻟﻲ ﺑﺪﻟﻴﻞ ﺍﻳﺠﺎﺩ ﺗﺪﺍﺧﻞ‪،‬‬
‫ﺍﻣﮑﺎﻥ ﻋﺪﻡ ﻣﻮﻓﻘﻴﺖ ﺩﺭ ﺍﺭﺳﺎﻝ ﻫﺎﻱ ﻣﺘﻌﺪﺩ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪.‬‬
‫ﺍﺯ ﻧﻈﺮ ﻓﻴﺰﻳﮑﻲ ﻣﻲ ﺗﻮﺍﻥ ﮐﺎﻧﺎﻝ ﻣﺸﺘﺮﮎ ﺭﺍ ﺑﺎ ﻳﮏ ﻣﺎﺗﺮﻳﺲ ﺍﺣﺘﻤﺎﻝ ] ‪ = [ρ‬ﻣﺪﻝ ﺳﺎﺯﻱ ﮐﺮﺩ ﮐﻪ ﺩﺭ ﺁﻥ ﺩﺭﺍﻳﻪ ‪ ρ‬ﻧﺸﺎﺩﻥ‬
‫ﺩﻫﻨﺪﻩ ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﺑﺴﺘﻪ ﺩﺍﺩﻩ ﺍﺳﺖ ﻫﻨﮕﺎﻣﻲ ﮐﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﻃﻮﺭ ﻫﻤﺰﻣﺎﻥ ﺑﺨﻮﺍﻫﻨﺪ ﺩﺭ ﻳﮏ ﺑﺎﺯﻩ ﺯﻣﺎﻧﻲ ﺍﻗﺪﺍﻡ ﺑﻪ‬
‫ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﮐﻨﻨﺪ‪ .‬ﺑﻨﺎﺑﺮ ﺍﻳﻦ ﺍﻣﻴﺪ ﺭﻳﺎﺿﻲ ﺗﻌﺪﺍﺩ ﺍﺭﺳﺎﻝ ﻫﺎﻱ ﻣﻮﻓﻖ ﺍﺯ ﺗﻌﺪﺍﺩ ﮐﻞ ﺑﺴﺘﻪ ﺍﺭﺳﺎﻟﻲ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
‫∑=‬
‫‪ρ‬‬
‫ﮐﻪ ﻃﺒﻖ ﺗﻘﺎﺭﻥ ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﺑﺮﺍﻱ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ‪ ρ /n‬ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﺩﺭ ﺍﻳﻨﺠﺎ ﺗﻨﻬﺎ ﺑﻪ ﺑﺮﺭﺳﻲ ﻳﮏ ﺣﺎﻟﺖ ﺧﺎﺹ‬
‫ﺍﺯ ﻣﺴﺎﻟﻪ ﻓﻮﻕ ﺧﻮﺍﻫﻴﻢ ﭘﺮﺩﺍﺧﺖ ﻭ ﺩﺭ ﺁﻥ ﻓﺮﺽ ﻣﻲ ﮐﻨﻴﻢ ﮐﻪ ﺗﻨﻬﺎ ﺍﻣﮑﺎﻥ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﻳﮏ ﺑﺴﺘﻪ ﺍﺯ ﮐﺎﻧﺎﻝ ﺩﺭ ﻫﺮ ﺑﺎﺯﻩ ﻭﺟﻮﺩ ﺩﺍﺷﺘﻪ‬
‫ﺑﺎﺷﺪ‪.‬‬
‫ﺷﺮﺡ ﺑﺎﺯﻱ ﻓﻮﻕ ﭼﻨﻴﻦ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ :‬ﺩﺭ ﺍﺑﺘﺪﺍ ‪ n‬ﻓﺮﺳﺘﻨﺪﻩ ﺑﺎﺯﻱ ﺭﺍ ﺷﺮﻭﻉ ﻣﻲ ﮐﻨﻨﺪ ﺍﻳﻦ ﺑﺎﺯﻱ ﺭﺍ ) ( ﻣﻲ ﻧﺎﻣﻴﻢ‪ .‬ﺍﮔﺮ ﺩﺭ ﺑﺎﺯﻩ ﺯﻣﺎﻧﻲ‬
‫ﺍﻭﻝ ﻓﻘﻂ ﻳﮑﻲ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﺩﺍﺩﻩ ﺧﻮﺩ ﮐﻨﺪ‪ ،‬ﺑﺴﺘﻪ ﺍﻭ ﺑﺎ ﻣﻮﻓﻘﻴﺖ ﺑﻪ ﻣﻘﺼﺪ ﺧﻮﺍﻫﺪ ﺭﺳﻴﺪ ﻭ ﺑﺎﺯﻱ ﺩﺭ ﻣﺮﺣﻠﻪ‬
‫ﺑﻌﺪ ﺑﺎ ‪ − 1‬ﻓﺮﺳﺘﻨﺪﻩ ﺩﻳﮕﺮ ﺩﻧﺒﺎﻝ ﺷﻮﺩ‪ ،‬ﻳﻌﻨﻲ )‪ . ( − 1‬ﻭﻟﻲ ﺍﮔﺮ ﻫﻴﭽﻴﮏ ﻳﺎ ﺑﻴﺶ ﺍﺯ ﻳﮑﻲ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ‬
‫ﺑﺴﺘﻪ ﻫﺎﻱ ﺧﻮﺩ ﺩﺭ ﻳﮏ ﺑﺎﺯﻩ ﺯﻣﺎﻧﻲ ﮐﻨﻨﺪ‪ ،‬ﻫﻴﭻ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻘﻲ ﺩﺭ ﺁﻥ ﺑﺎﺯﻩ ﺍﻧﺠﺎﻡ ﻧﻤﻲ ﺷﻮﺩ ﻭ ﺑﺎﺯﻱ ) ( ﺩﺭ ﻣﺮﺣﻠﻪ ﺑﻌﺪ ﺗﮑﺮﺍﺭ‬
‫ﺧﻮﺍﻫﺪ ﺷﺪ‪.‬‬
‫ﭘﺲ ﻫﺮﻳﮏ ﺍﺯ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻳﻦ ﺑﺎﺯﻱ ﺩﺭ ﻫﺮﻣﺮﺣﻠﻪ ‪ 2‬ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﻮﺍﻫﻨﺪ ﺩﺍﺷﺖ‪ :‬ﺍﺭﺳﺎﻝ )‪ (T‬ﻳﺎ ﻋﺪﻡ ﺍﺭﺳﺎﻝ )‪ .(w‬ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﮔﻔﺘﻪ‬
‫ﺷﺪ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻋﻼﻗﻤﻨﺪﻧﺪ ﮐﻪ ﺩﺍﺩﻩ ﺧﻮﺩ ﺭﺍ ﺑﺎ ﮐﻤﺘﺮﻳﻦ ﺗﺎﺧﻴﺮ ﺑﻔﺮﺳﺘﻨﺪ‪ .‬ﺑﺮﺍﻱ ﻣﺪﻝ ﺳﺎﺯﻱ ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﻳﮏ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﮐﻤﺘﺮ‬
‫ﺍﺯ ﻳﮏ ﺑﺮﺍﻱ ﺍﻳﻦ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﺗﺎﺑﻊ ﺳﻮﺩ ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﻧﺴﺒﺖ ﺑﻪ ﻣﺮﺣﻠﻪ ﻗﺒﻞ ﺩﺭ ﺁﻥ ﺿﺮﺏ ﺷﻮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ‬
‫ﺍﮔﺮ ﺳﻮﺩ ﺍﺭﺳﺎﻝ ﻣﻮﻓﻖ ﺍﺯ ﮐﺎﻧﺎﻝ ﺭﺍ ‪ 1‬ﻭﺍﺣﺪ ﻭ ﺭﺍ ﺗﻌﺪﺍﺩ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎﻳﻲ ﮐﻪ ﺩﺭ ﻳﮏ ﺑﺎﺯﻩ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺍﺯ ﮐﺎﻧﺎﻝ ﻣﻲ ﮐﻨﻨﺪ‬
‫ﺑﮕﻴﺮﻳﻢ‪ ،‬ﺗﺎﺑﻊ ﺳﻮﺩ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺻﻮﺭﺕ ﺑﺎﺯﮔﺸﺘﻲ ﺯﻳﺮ ﻧﻮﺷﺖ‪:‬‬
‫]‪[ > 0‬‬
‫ﮐﻪ ﺩﺭ ﺁﻥ‬
‫‪,‬‬
‫]‪[ ≠ 1‬‬
‫‪,‬‬
‫‪,‬‬
‫‪= 0] +‬‬
‫‪= 1] +‬‬
‫ﺗﺎﺑﻊ ﺑﻬﺮﻩ ﻧﻔﺮ ‪ i‬ﺍﻡ ﺩﺭ ﺑﺎﺯﻱ )‪ G(n‬ﺍﺳﺖ ﻭ ﺩﺍﺭﻳﻢ‪:‬‬
‫‪7‬‬
‫[‬
‫[ =) (‬
‫‪,‬‬
‫‪,‬‬
‫=) (‬
‫‪,‬‬
‫) (‬
‫ﻭ ﻳﺎ ﻣﻌﺎﺩﻻ ﺩﺍﺭﻳﻢ‪:‬‬
‫‪,‬‬
‫‪( ).‬‬
‫]‬
‫‪,‬‬
‫‪( )+‬‬
‫‪,‬‬
‫[‬
‫]‬
‫[ ‪.‬‬
‫]‬
‫]‬
‫[ ‪.‬‬
‫[ ‪.‬‬
‫‪( ).‬‬
‫‪,‬‬
‫=) (‬
‫‪,‬‬
‫=‬
‫‪,‬‬
‫‪,‬‬
‫=) (‬
‫‪,‬‬
‫ﺍﺳﺘﺮﺍﺗﮋﻱ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺭﺍ ﺍﻳﺴﺘﺎﻥ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ‪ ،‬ﺑﻪ ﻃﻮﺭﻱ ﮐﻪ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺑﻪ ﻋﻨﻮﺍﻥ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﻮﺩ ﺑﺮﺩﺍﺭ ﺍﺣﺘﻤﺎﻟﻲ ﺑﻪ ﺻﻮﺭﺕ‬
‫‪,‬‬
‫‪,…,‬‬
‫‪,‬‬
‫‪,‬‬
‫‪,‬‬
‫=‬
‫ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﮐﻨﺪ ﮐﻪ ﺩﺭ ﺁﻥ‬
‫ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﻓﺮﺳﺘﻨﺪﻩ ‪ i‬ﺍﻡ ﺩﺭ ﺑﺎﺯﻱ )‪ G(k‬ﺍﺳﺖ‪.‬‬
‫‪,‬‬
‫ﺍﻳﻦ ﺑﺎﺯﻱ ﺩﺍﺭﺍﻱ ﺗﻌﺎﺩﻝ ﻫﺎﻱ ﺯﻳﺎﺩﻱ ﺍﺳﺖ‪ ،‬ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺑﻪ ﺭﺍﺣﺘﻲ ﻣﻲ ﺗﻮﺍﻥ ﺩﻳﺪ ﮐﻪ ﻳﮑﻲ ﺍﺯ ﺗﻌﺎﺩﻝ ﻫﺎ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﻧﻔﺮ ‪ i‬ﺍﻡ ﺩﺭ ﺑﺎﺯﻩ ‪i‬‬
‫ﺍﻡ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺧﻮﺩ ﮐﻨﺪ ﻳﻌﻨﻲ ﻫﻤﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺧﺎﻟﺺ‬
‫‪=1‬‬
‫≠ ∀‪= 0 ,‬‬
‫‪,‬‬
‫‪,‬‬
‫ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﮐﻨﻨﺪ )ﺑﺪﻳﻦ ﺗﺮﺗﻴﺐ ﺣﺪﺍﻗﻞ !‪ n‬ﺗﻌﺎﺩﻝ ﻣﺘﻨﺎﻇﺮ ﺑﺎ ﻫﺮﻳﮏ ﺍﺯ ﺟﺎﻳﮕﺸﺖ ﻫﺎﻱ ‪ n‬ﻓﺮﺳﺘﻨﺪﻩ ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ(‪.‬‬
‫ﻭﻟﻲ ﺍﺯ ﺁﻧﺠﺎ ﮐﻪ ﻫﻴﭻ ﺗﻤﺎﻳﺰﻱ ﺑﻴﻦ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻭﺟﻮﺩ ﻧﺪﺍﺭﺩ‪ ،‬ﺩﺭ ﺻﻮﺭﺕ ﻭﺟﻮﺩ ﻣﺎﻳﻞ ﺑﻪ ﻳﺎﻓﺘﻦ ﺗﻌﺎﺩﻝ ﻣﻨﺼﻔﺎﻧﻪ ﺑﺎﺯﻱ ﻫﺴﺘﻴﻢ ﮐﻪ ﺩﺭ‬
‫ﺁﻥ ﺑﺮﺩﺍﺭ ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻫﻤﻪ ﻳﮑﻲ ﺑﺎﺷﺪ‪ .‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﺑﺎﺯﻱ )‪ G(n‬ﺩﺍﺭﺍﻱ ﺗﻌﺎﺩﻝ ﻣﻨﺼﻔﺎﻧﻪ ﻳﮑﺘﺎﺳﺖ‪ .‬ﺩﺭﺍﻳﻪ‬
‫ﻫﺎﻱ ﺑﺮﺩﺍﺭ ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﺑﺮﺍﻱ ﺗﻌﺎﺩﻝ ﻣﻨﺼﻔﺎﻧﻪ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﮐﻤﮏ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﮐﺎﻣﭙﻴﻮﺗﺮﻱ ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﺑﺮﺍﻱ ‪3‬‬
‫ﻣﻘﺪﺍﺭ ﻣﺘﻔﺎﻭﺕ ﺍﺯ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﺩﺭ ﺷﮑﻞ ﺯﻳﺮ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪:‬‬
‫ﺑﺎ ﻭﺟﻮﺩ ﮐﺎﻫﺶ‬
‫ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﺍﺯ ﺷﮑﻞ ﭘﻴﺪﺍﺳﺖ ﺑﺮﺍﻱ ﻫﺮ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﮐﻤﺘﺮ ﺍﺯ ﻳﮏ‪ ،‬ﺍﺣﺘﻤﺎﻝ ﺍﺭﺳﺎﻝ ﺩﺭ ﺑﺎﺯﻱ )‪ G(n‬ﻳﻌﻨﻲ‬
‫ﺍﻭﻟﻴﻪ ﺩﺭ ﻧﻬﺎﻳﺖ ﺍﺯ ﺟﺎﻳﻲ ﺑﻪ ﺑﻌﺪ ﺑﻪ ‪ 1‬ﻣﻲ ﺭﺳﺪ ﻭ ﺍﻳﻦ ﺑﺪﻳﻦ ﻣﻌﻨﺎﺳﺖ ﮐﻪ ﻭﻗﺘﻲ ﺗﻌﺪﺍﺩ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺯﻳﺎﺩ ﺷﻮﺩ‪ ،‬ﻫﻤﻪ ﺑﺎ ﺍﺣﺘﻤﺎﻝ ‪ 1‬ﺩﺭ‬
‫ﺗﻤﺎﻣﻲ ﺑﺎﺯﻩ ﻫﺎﻱ ﺯﻣﺎﻧﻲ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﺧﻮﺍﻫﻨﺪ ﮐﺮﺩ! ﭘﺲ ﺍﮔﺮ ﺗﻌﺪﺍﺩﻱ ﻓﺮﺳﺘﻨﺪﻩ ﺑﺎ ﺷﺮﺍﻳﻂ ﺑﺎﺯﻱ ﻓﻮﻕ‬
‫ﺑﺨﻮﺍﻫﻨﺪ ﺧﻮﺩﺧﻮﺍﻫﺎﻧﻪ ﺗﺎﺑﻊ ﺳﻮﺩ ﺧﻮﺩ ﺭﺍ ﺣﺪﺍﮐﺜﺮ ﮐﻨﻨﺪ‪ ،‬ﺷﺒﮑﻪ ﭘﺎﻳﺪﺍﺭ ﻧﺨﻮﺍﻫﺪ ﺑﻮﺩ ﻭ ﺣﺘﻲ ﻳﮏ ﺑﺴﺘﻪ ﻫﻢ ﺑﺎ ﻣﻮﻓﻘﻴﺖ ﺍﺭﺳﺎﻝ ﻧﺨﻮﺍﻫﺪ‬
‫ﺷﺪ‪.‬‬
‫‪8‬‬
‫ﺍﻳﻦ ﻧﺘﻴﺠﻪ ﭼﻨﺪﺍﻥ ﺩﻭﺭ ﺍﺯ ﺍﻧﺘﻈﺎﺭ ﻧﺒﻮﺩ ﺯﻳﺮﺍ ﺩﺭ ﻣﺪﻝ ﺳﺎﺯﻱ ﺧﻮﺩ ﻫﻴﭻ ﻫﺰﻳﻨﻪ ﺍﻱ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﻧﺎﻣﻔﻖ ﺩﺭ ﻧﻈﺮ ﻧﮕﺮﻓﺘﻴﻢ‪ .‬ﺣﺎﻝ ﻣﺪﻝ‬
‫ﺳﺎﺯﻱ ﺧﻮﺩ ﺭﺍ ﻭﺍﻗﻌﻲ ﺗﺮ ﻣﻲ ﮐﻨﻴﻢ ﻭ ﺩﺭ ﺁﻥ ﻫﺰﻳﻨﻪ ‪ 0 < ≪ 1‬ﺭﺍ ﻧﻴﺰﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎ ﻣﺘﻨﺎﻇﺮ ﺑﺎ ﺗﻮﺍﻥ ﻣﺼﺮﻓﻲ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ‬
‫ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ‪ .‬ﺑﻪ ﻃﺮﻳﻘﻲ ﻣﺸﺎﺑﻪ ﻣﻲ ﺗﻮﺍﻥ ﻧﻮﺷﺖ‪:‬‬
‫]‬
‫]‬
‫[ ‪.‬‬
‫[‬
‫=) (‬
‫‪,‬‬
‫ﺷﮑﻞ ﺯﻳﺮ ﻧﺘﺎﻳﺞ ﺣﺎﺻﻞ ﺑﺮﺍﻱ ﺗﻌﺎﺩﻝ ﻧﺶ ﻣﻨﺼﻔﺎﻧﻪ ﺑﺎ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ‪ δ = 0.95‬ﻭ ﻣﻘﺎﺩﻳﺮ ﻣﺨﺘﻠﻒ ‪ c‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪:‬‬
‫ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﮐﻨﻴﺪ ﺍﻳﻦ ﻧﻤﻮﺩﺍﺭ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ ﮐﻪ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﭘﺎﺭﺍﻣﺘﺮ ﻫﺰﻳﻨﻪ ﺍﺭﺳﺎﻝ ﻣﻮﺟﺐ ﻣﻲ ﺷﻮﺩ ﺗﺎ ﺩﻳﮕﺮ ﺍﺣﺘﻤﺎﻝ‬
‫ﺍﺭﺳﺎﻝ ﺑﻪ ‪ 1‬ﻣﻴﻞ ﻧﮑﻨﺪ‪ .‬ﺍﻳﻦ ﻧﺘﻴﺠﻪ ﺍﺯ ﺩﻳﺪﮔﺎﻩ ﮐﺎﺭﺑﺮﺩﻱ ﺑﺴﻴﺎﺭ ﺟﺎﻟﺐ ﺗﻮﺟﻪ ﺍﺳﺖ‪ ،‬ﺯﻳﺮﺍ ﺑﻴﺎﻥ ﻣﻲ ﺩﺍﺭﺩ ﮐﻪ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﻧﺎﻣﺘﻤﺮﮐﺰ‬
‫ﺩﺭ ﺑﺪﺗﺮﻳﻦ ﺷﺮﺍﻳﻂ ﮐﻪ ﺩﺭ ﺁﻥ ﺗﻤﺎﻡ ﮐﺎﺭﺑﺮﺍﻥ ﺑﺨﻮﺍﻫﻨﺪ ﺧﻮﺩﺧﻮﺍﻫﺎﻧﻪ ﻋﻤﻞ ﮐﻨﻨﺪ ﻧﻴﺰ ﭘﺎﻳﺪﺍﺭ ﻣﻲ ﻣﺎﻧﺪ‪.‬‬
‫‪ -2-4‬ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﮐﻨﺘﺮﻝ ﺗﻮﺍﻥ‬
‫ﺩﺭ ﺍﻳﻦ ﻗﺴﻤﺖ ﻣﻲ ﺧﻮﺍﻫﻴﻢ ﺑﻪ ﺑﺮﺭﺳﻲ ﻳﮑﻲ ﺩﻳﮕﺮ ﺍﺯ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﻣﻬﻢ ﺷﺒﮑﻪ ﺑﭙﺮﺩﺍﺯﻳﻢ‪ .‬ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﻣﻲ ﺩﺍﻧﻴﺪ ﻳﮑﻲ ﺍﺯ‬
‫ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﻣﻬﻢ ﺗﻌﻴﻴﻦ ﮐﻨﻨﺪﻩ ﻱ ﺍﺣﺘﻤﺎﻝ ﺧﻄﺎ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ‪ CDMA‬ﭘﺎﺭﺍﻣﺘﺮ ‪ SINR‬ﻳﺎ ﻫﻤﺎﻥ ﻧﺴﺒﺖ ﺗﻮﺍﻥ ﺳﻴﮕﻨﺎﻝ ﺑﻪ ﺗﺪﺍﺧﻞ ﻭ ﻧﻮﻳﺰ‬
‫ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮ ﺑﺎ ﺗﻮﺍﻥ ﺍﺭﺳﺎﻟﻲ ﺩﺍﺩﻩ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻪ ﻃﻮﺭ ﻣﺴﺘﻘﻴﻢ ﻭ ﺑﺎ ﻣﺠﻤﻮﻉ ﺗﻮﺍﻥ ﻫﺎﻱ ﺗﺪﺍﺧﻠﻲ ﺩﺭﻳﺎﻓﺘﻲ ﻧﺎﺷﻲ ﺍﺯ ﺍﺭﺗﺒﺎﻃﺎﺕ ﺳﺎﻳﺮ‬
‫ﮐﺎﺭﺑﺮﺍﻥ ﺩﺭ ﮔﻴﺮﻧﺪﻩ ﻣﺮﺑﻮﻃﻪ‪ ،‬ﺑﻪ ﻃﻮﺭ ﻣﻌﮑﻮﺱ ﺭﺍﺑﻄﻪ ﺩﺍﺭﺩ‪.‬‬
‫ﭘﺲ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺑﺮﺍﻱ ﺑﺎﻻﺑﺮﺩﻥ ﭘﺎﺭﺍﻣﺘﺮ ‪ SINR‬ﺧﻮﺩ ﻣﺎﻳﻞ ﺍﺳﺖ ﺗﺎ ﺗﻮﺍﻥ ﺍﺭﺳﺎﻟﻲ ﺧﻮﺩ ﺭﺍ ﺍﻓﺰﺍﻳﺶ ﺩﻫﺪ ﻭﻟﻲ ﺍﻳﻦ ﮐﺎﺭ ﻣﻨﺠﺮ ﺑﻪ‬
‫ﺍﻓﺰﺍﻳﺶ ﺗﺪﺍﺧﻞ ﺑﺮﺍﻱ ﺳﺎﻳﺮ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﺑﻲ ﺳﻴﻢ ﺧﻮﺍﻫﺪ ﺷﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻳﻦ ﺑﺎﺯﻱ ﻫﻢ ﺩﺍﺭﺍﻱ ﻣﻨﺎﻓﻊ ﻣﺘﻀﺎﺩ ﻫﺴﺘﻨﺪ‪.‬‬
‫ﺣﺎﻝ ﻓﺮﺽ ﮐﻨﻴﺪ ﮐﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺑﻲ ﺳﻴﻢ ﺩﺭ ﻳﮏ ﺷﺒﮑﻪ ‪ CDMA‬ﺑﺨﻮﺍﻫﻨﺪ ﺑﻪ ﻃﻮﺭ ﻫﻤﺰﻣﺎﻥ ﺑﻪ ﻳﮏ ﻣﻘﺼﺪ ﻣﺸﺘﺮﮎ )ﻣﺎﻧﻨﺪ ‪ BTS‬ﺩﺭ‬
‫ﺷﺒﮑﻪ ﻣﻮﺑﺎﻳﻞ( ﺩﺍﺩﻩ ﺍﺭﺳﺎﻝ ﮐﻨﻨﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻓﺮﺽ ﮐﻨﻴﺪ ﮐﻪ ﺗﻮﺍﻧﻲ ﺑﺎﺷﺪ ﮐﻪ ﻧﻔﺮ ‪ j‬ﺍﻡ ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺧﻮﺩ ﺑﻪ ﻃﻮﺭ ﭘﻴﻮﺳﺘﻪ ﺩﺭ ﺑﺎﺯﻩ‬
‫ﺑﺎﺷﺪ ﻭﻫﻤﭽﻨﻴﻦ ﺍﺯ ﻣﺪﻭﻻﺳﻴﻮﻥ‬
‫]∞ ‪ [0,‬ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﮐﻨﺪ‪ .‬ﺍﮔﺮ ﻃﻮﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ‪ L‬ﺑﻮﺩﻩ ﻭ ﻧﺮﺥ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻫﺎ‬
‫‪/‬‬
‫‪ FSK‬ﺑﺮﺍﻱ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻫﺎ ﺑﻪ ﮐﺎﺭ ﮔﺮﻓﺘﻪ ﺷﻮﺩ‪ ،‬ﻣﻲ ﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﮐﻪ ﺗﺎﺑﻊ ﺳﻮﺩ ﺯﻳﺮ ﻣﺪﻝ ﻣﻨﺎﺳﺒﻲ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪:‬‬
‫)‬
‫‪.‬‬
‫‪(1 −‬‬
‫‪9‬‬
‫=‬
‫‪,‬‬
‫ﮐﻪ ﺩﺭ ﺁﻥ‬
‫ﭘﺎﺭﺍﻣﺘﺮ ‪ SINR‬ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻔﺮ ‪ j‬ﺍﻡ ﺍﺳﺖ‪.‬‬
‫ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﺑﺎﺯﻱ ﻓﻮﻕ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﻱ ﺩﺍﺭﺍﻱ ﺗﻌﺎﺩﻝ ﻧﺶ ﻳﮑﺘﺎﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﻤﻪ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﻣﺴﺘﻘﻞ ﺍﺯ ﻓﺎﺻﻠﻪ‬
‫ﺧﻮﺩ‪ ،‬ﻧﺴﺒﺖ ‪ SINR‬ﻳﮑﺴﺎﻧﻲ ﺩﺭ ﺍﻳﺴﺘﮕﺎﻩ ﮔﻴﺮﻧﺪﻩ ﺧﻮﺍﻫﻨﺪ ﺩﺍﺷﺖ‪ ،‬ﻳﻌﻨﻲ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱ ﻣﻨﺼﻔﺎﻧﻪ ﺍﺳﺖ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﻣﻨﺼﻔﺎﻧﻪ ﺑﻮﺩﻥ ﺗﻌﺎﺩﻝ‬
‫ﻫﺎ‪ ،‬ﻣﺎﻳﻠﻴﻢ ﮐﻪ ﺁﻧﻬﺎ ﺑﻬﻴﻨﻪ ﻧﻴﺰ ﺑﺎﺷﻨﺪ ﻳﮑﻲ ﺍﺯ ﻣﻌﻴﺎﺭﻫﺎﻱ ﻣﻬﻢ ﺑﻬﻴﻨﻪ ﺑﻮﺩﻥ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﻫﺎ ﺑﻬﻴﻨﻪ ﺑﻮﺩﻥ ﭘﺎﺭﺗﻮ ﺍﺳﺖ‪.‬‬
‫ﺗﻌﺮﻳﻒ‪ :‬ﻳﮏ ﻣﺠﻤﻮﻋﻪ ﺍﺳﺘﺮﺍﺗﮋﻱ ﺑﺮﺍﻱ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺯ ﺑﻬﻴﻨﻪ ﭘﺎﺭﺗﻮ ﺍﺳﺖ ﺍﮔﺮ ﻭ ﻓﻘﻂ ﺍﮔﺮ ﻫﻴﭻ ﻣﺠﻤﻮﻋﻪ ﺩﻳﮕﺮﻱ ﺍﺯ ﺍﺳﺘﺮﺍﺗﮋﻱ ﻫﺎ ﻧﺘﻮﺍﻥ ﻳﺎﻓﺖ ﮐﻪ‬
‫ﺩﺭ ﺳﻮﺩ ﻳﮑﻲ ﺍﺯ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺪﻭﻥ ﮐﺎﺳﺘﻦ ﺍﺯ ﺳﻮﺩ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻓﺰﺍﻳﺶ ﻳﺎﻓﺘﻪ ﺑﺎﺷﺪ‪.‬‬
‫ﺑﻄﻮﺭ ﻃﺒﻴﻌﻲ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ﻣﺘﻤﺮﮐﺰ‪ ،‬ﮐﻨﺘﺮﻝ ﺗﻮﺍﻥ ﺑﻪ ﻃﻮﺭ ﺑﻬﻴﻨﻪ ﺍﻧﺠﺎﻡ ﻣﻲ ﮔﻴﺮﺩ ﻭﻟﻲ ﻣﺘﺎﺳﻔﺎﻧﻪ ﻣﻲ ﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﮐﻪ ﺗﻌﺎﺩﻝ‬
‫ﻧﺶ ﺑﺎﺯﻱ ﻓﻮﻕ ﺧﺎﺻﻴﺖ ﺑﻬﻴﻨﮕﻲ ﭘﺎﺭﺗﻮ ﺭﺍ ﻧﺪﺍﺭﺩ‪ .‬ﺣﺎﻝ ﺑﺎﺯﻱ ﻓﻮﻕ ﺭﺍ ﺩﺭ ﺣﺎﻟﺖ ﭘﻲ ﺩﺭ ﭘﻲ ﺑﺮﺭﺳﻲ ﻣﻲ ﮐﻨﻴﻢ‪ .‬ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﻲ‬
‫ﺧﻮﺍﻫﻨﺪ ﻣﺠﻤﻮﻉ ﮐﻠﻲ ﺳﻮﺩ ﺧﻮﺩ ﺭﺍ ﺩﺭ ﺗﻤﺎﻣﻲ ﻣﺮﺍﺣﻞ ﺑﺎﺯﻱ ﺣﺪﺍﮐﺜﺮ ﮐﻨﻨﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﻓﺮﺽ ﻣﻲ ﮐﻨﻴﻢ ﮐﻪ ﺑﺎﺯﻱ ﻧﺎﻣﺘﻨﺎﻫﻲ ﺑﻮﺩﻩ ﻭ ﺩﺭ ﺁﻥ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﻫﻴﭻ ﺍﻃﻼﻋﻲ ﺍﺯ ﺯﻣﺎﻥ ﭘﺎﻳﺎﻥ ﺑﺎﺯﻱ ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﻨﺪ‪.‬‬
‫ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺗﻌﺮﻳﻒ ﺷﺪﻩ ﻓﻮﻕ‪ ،‬ﺗﻌﺪﺍﺩ ﺯﻳﺎﺩﻱ ﺗﻌﺎﺩﻝ ﻧﺶ ﺧﻮﺍﻫﺪ ﺩﺍﺷﺖ‪ ،‬ﺩﺭ ﺣﻘﻴﻘﺖ ﻳﮑﻲ ﺍﺯ ﻗﻀﻴﻪ ﻫﺎﻱ ﻣﻬﻢ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﻫﺎ ﺑﻴﺎﻥ ﻣﻲ‬
‫ﺩﺍﺭﺩ ﮐﻪ ﺍﮔﺮ ﺿﺮﻳﺐ ﺗﺨﻔﻴﻒ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺑﻪ ﺍﻧﺪﺍﺯﻩ ﮐﺎﻓﻲ ﻧﺰﺩﻳﮏ ‪ 1‬ﺑﺎﺷﺪ‪ ،‬ﻫﺮﻳﮏ ﺍﺯ ﻧﻘﺎﻁ ﻣﺠﻤﻮﻋﻪ ﺩﺳﺖ ﻳﺎﻓﺘﻨﻲ ﺳﻮﺩ ﻫﺎ‪ ،‬ﻣﻲ ﺗﻮﺍﻧﺪ‬
‫ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﺑﺎﺷﺪ‪ .‬ﺣﺎﻝ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﻧﺘﺨﺎﺏ ﮐﺮﺩ ﮐﻪ ﻣﻨﺼﻔﺎﻧﻪ ﻭ ﺑﻬﻴﻨﻪ ﭘﺎﺭﺗﻮ ﺑﺎﺷﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺩﺭ ﻧﻈﺮ‬
‫ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺑﺮﺍﻱ ﺗﻨﺒﻴﻪ ﻓﺮﺳﺘﻨﺪﻩ ﺍﻱ ﮐﻪ ﺩﺭ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﺯ ﺑﺎﺯﻱ ﺗﻮﺍﻥ ﺑﻴﺸﺘﺮﻱ ﺍﺯ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﻣﺪ ﻧﻈﺮ ﺍﻧﺘﺨﺎﺏ ﮐﻨﺪ‪ ،‬ﺩﺭ‬
‫ﻣﺮﺣﻠﻪ ﺑﻌﺪ ﺑﺎﺯﻱ ﺑﺎ ﺗﻮﺍﻥ ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﻱ ﺍﻗﺪﺍﻡ ﺑﻪ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﻫﺎﻱ ﺧﻮﺩ ﮐﻨﻨﺪ )ﺩﺭ ﺍﻳﻨﺠﺎ ﻓﺮﺽ ﻣﻲ ﺷﻮﺩ ﮐﻪ‬
‫ﺍﻳﺴﺘﮕﺎﻩ ﮔﻴﺮﻧﺪﻩ ﺗﻮﺍﻥ ﺍﺭﺳﺎﻟﻲ ﻫﺮﻳﮏ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺭﺍ ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﺍﺯ ﺑﺎﺯﻱ ﺑﻪ ﺍﻃﻼﻉ ﺳﺎﻳﺮ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺑﺮﺳﺎﻧﺪ(‪.‬‬
‫ﺷﮑﻞ ﻫﺎﻱ ﺯﻳﺮ ﻣﻘﺎﻳﺴﻪ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﻳﮏ ﻣﺮﺣﻠﻪ ﺍﻱ ﻭ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﺗﻮﺻﻴﻒ ﺷﺪﻩ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﻨﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻫﺎ‬
‫ﺗﻮﺯﻳﻊ ﮐﺎﺭﺑﺮﺍﻥ ﺑﻪ ﻃﻮﺭ ﻳﮑﻨﻮﺍﺧﺖ ﺩﺭ ﺷﻌﺎﻉ ‪ 5km‬ﺍﻱ ﺍﻳﺴﺘﮕﺎﻩ ﮔﻴﺮﻧﺪﻩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﺩﺭ ﺷﮑﻞ ﻣﻲ ﺑﻴﻨﻴﺪ ﺩﺭ ﺑﺎﺯﻱ ﭘﻲ ﺩﺭ ﭘﻲ ﻋﻼﻭﻩ ﺑﺮ ﺍﺗﻼﻑ ﺗﻮﺍﻥ ﮐﻤﺘﺮ‪ ،‬ﺗﺎﺑﻊ ﺳﻮﺩ ﻣﻘﺪﺍﺭ ﺑﻴﺸﺘﺮﻱ ﺑﺮﺍﻱ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺍﺭﺩ )ﺑﻬﻴﻨﻪ‬
‫ﺗﺮ ﺍﺳﺖ(‪.‬‬
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‫‪ -5‬ﺍﺷﺎﺭﻩ ﺍﻱ ﺑﻪ ﭼﻨﺪ ﺑﺎﺯﻱ ﻣﻬﻢ ﺩﻳﮕﺮ‬
‫‪ -1-5‬ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺩﺭ ﺷﺒﮑﻪ‬
‫ﻳﮑﻲ ﺩﻳﮕﺮ ﺍﺯ ﺑﺎﺯﻱ ﻫﺎﻱ ﭘﺮ ﮐﺎﺭﺑﺮﺩ ﺩﻳﮕﺮ ﺷﺒﮑﻪ ﻫﺎ ﮐﻪ ﺗﺎ ﮐﻨﻮﻥ ﺑﺎ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﺑﻪ ﺧﻮﺑﻲ ﻣﺪﻝ ﺳﺎﺯﻱ ﻭﺑﺮﺭﺳﻲ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ‬
‫ﺍﺳﺖ‪ .‬ﻓﺮﺽ ﮐﻨﻴﺪ ﺩﺭ ﻳﮏ ﺷﺒﮑﻪ ﺩﻳﺘﺎﮔﺮﺍﻡ ﻣﺎﻧﻨﺪ ﺷﺒﮑﻪ ﺍﻳﻨﺘﺮﻧﺖ‪ ،‬ﺗﻌﻴﻴﻦ ﻣﺴﻴﺮ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺍﺯ ﻣﺒﺪﺍ ﺗﺎ ﻣﻘﺼﺪ ﺑﻪ ﻋﻬﺪﻩ ﻓﺮﺳﺘﻨﺪﻩ ﺑﺎﺷﺪ ‪.‬‬
‫ﺣﺎﻝ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺭﺍ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﺩﺭ ﻧﻈﺮ ﺑﮕﻴﻴﺮﻳﺪ ﮐﻪ ﻫﺮ ﮐﺪﺍﻡ ﻣﺎﻳﻠﻨﺪ ﺑﺴﺘﻪ ﻫﺎﻳﺸﺎﻥ ﺑﺎ ﮐﻤﺘﺮﻳﻦ ﺗﺎﺧﻴﺮ ﺑﻪ ﻣﻘﺼﺪ‬
‫ﺑﺮﺳﺪ‪.‬‬
‫ﺍﮔﺮ ﺩﺭ ﺷﺒﮑﻪ ﺗﻨﻬﺎ ﻳﮏ ﻓﺮﺳﺘﻨﺪﻩ ﻭﺟﻮﺩ ﺩﺍﺷﺖ ﻭ ﻳﺎ ﺍﻳﻨﮑﻪ ﻣﺴﻴﺮﻫﺎﻱ ﻣﻤﮑﻦ ﺑﺮﺍﻱ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﮐﺎﻣﻼ ﺍﺯ ﻳﮑﺪﻳﮕﺮ ﻣﺠﺰﺍ ﺑﻮﺩﻧﺪ‪،‬‬
‫ﺁﻥ ﮔﺎﻩ ﻣﺴﺎﻟﻪ ﻣﺴﻴﺮﻳﺎﺑﻲ ﺑﺮﺍﻱ ﺑﺴﺘﻪ ﻫﺎ ﺩﺭ ﺷﺒﮑﻪ ﺗﺒﺪﻳﻞ ﺑﻪ ﻳﮏ ﻣﺴﺎﻟﻪ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﺳﺎﺩﻩ ﺑﺮﺍﻱ ﻳﺎﻓﺘﻦ ﮐﻮﺗﺎﻩ ﺗﺮﻳﻦ ﻣﺴﻴﺮ ﺍﺯ ﻣﺒﺪﺍ ﺑﻪ‬
‫ﻣﻘﺼﺪ ﺩﺭ ﺷﺒﮑﻪ ﻣﻲ ﺷﺪ‪ .‬ﻭﻟﻲ ﺩﺭ ﺣﺎﻟﺖ ﮐﻠﻲ ﻫﺮﻳﮏ ﺍﺯ ﻟﻴﻨﮏ ﻫﺎﻱ ﺷﺒﮑﻪ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺑﻴﻦ ﭼﻨﺪ ﻣﺴﻴﺮ ﻣﺨﺘﻠﻒ ﺍﺯ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺗﺎ ﮔﻴﺮﻧﺪﻩ‬
‫ﻫﺎ‪ ،‬ﻣﺸﺘﺮﮎ ﺑﺎﺷﻨﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻫﺮﭼﻪ ﺗﻌﺪﺍﺩ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎﻱ ﺑﻴﺸﺘﺮﻱ ﺍﺯ ﻳﮏ ﻟﻴﻨﮏ ﺷﺒﮑﻪ ﺍﺳﺘﻔﺎﺩﻩ ﮐﻨﻨﺪ‪ ،‬ﺳﺮﻋﺖ ﺍﻧﺘﻘﺎﻝ ﺑﺴﺘﻪ ﻫﺎ ﺍﺯ‬
‫ﺁﻥ ﻟﻴﻨﮏ ﮐﺎﻫﺶ ﻣﻲ ﻳﺎﺑﺪ‪ .‬ﻫﻤﻴﻦ ﻭﺍﺑﺴﺘﮕﻲ ﺑﻴﻦ ﻣﺴﻴﺮ ﻫﺎ ﻣﻮﺟﺐ ﻣﻲ ﺷﻮﺩ ﺗﺎ ﻣﺴﺎﻟﻪ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺑﻴﻦ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ‬
‫ﺷﺒﮑﻪ ﺩﺭﺁﻳﺪ‪.‬‬
‫ﺩﺭ ﺍﻳﻨﺠﺎ ﺗﻨﻬﺎ ﺑﻪ ﺫﮐﺮ ﻳﮑﻲ ﺍﺯ ﻧﺘﺎﻳﺞ ﺟﺎﻟﺐ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﺑﺮﺭﺳﻲ ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﻳﻌﻨﻲ ﭘﺎﺭﺍﺩﻭﮐﺲ ﺑﺮﻳﺲ ﺑﺴﻨﺪﻩ ﻣﻲ ﮐﻨﻴﻢ‪ .‬ﻓﺮﺽ ﮐﻨﻴﺪ‬
‫ﻳﮏ ﺑﺎﺯﻱ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺩﺭ ﺷﺒﮑﻪ ﺑﻪ ﺗﻌﺎﺩﻝ ﺭﺳﻴﺪﻩ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﻃﻮﺭ ﺍﻧﺘﻈﺎﺭ ﺩﺍﺭﻳﻢ ﮐﻪ ﺑﺎ ﺍﻓﺰﻭﺩﻥ ﻟﻴﻨﮏ ﻫﺎﻱ ﺟﺪﻳﺪ ﺑﻪ ﺷﺒﮑﻪ‪ ،‬ﮐﺎﺭﺍﻳﻲ ﺷﺒﮑﻪ‬
‫ﺍﻓﺰﻭﺩﻩ ﺷﻮﺩ‪ ،‬ﻳﻌﻨﻲ ﺑﺴﺘﻪ ﻫﺎ ﺑﻪ ﻃﻮﺭ ﻣﺘﻮﺳﻂ ﺑﺎ ﺗﺎﺧﻴﺮ ﮐﻤﺘﺮﻱ ﺩﺭ ﺷﺒﮑﻪ ﺟﺮﻳﺎﻥ ﭘﻴﺪﺍ ﮐﻨﻨﺪ‪ ،‬ﻭﻟﻲ ﻣﻲ ﺗﻮﺍﻥ ﻣﺜﺎﻝ ﻫﺎﻳﻲ ﺁﻭﺭﺩ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺎ‬
‫ﺍﻓﺰﻭﺩﻥ ﻟﻴﻨﮏ ﺑﻪ ﺷﺒﮑﻪ ﻣﻨﺠﺮ ﺑﻪ ﮐﺎﻫﺶ ﮐﺎﺭﺍﻳﻲ ﺷﺒﮑﻪ ﺷﻮﺩ‪.‬‬
‫‪ -2-5‬ﺑﺎﺯﻱ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ‬
‫ﻋﺮﺿﻪ ﺳﺮﻭﻳﺲ ﻫﺎﻳﻲ ﺑﺎ ﺳﻄﻮﺡ ﮐﻴﻔﻴﺖ ﻣﺘﻔﺎﻭﺕ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎ‪ ،‬ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺭﺍ ﻣﻄﺮﺡ ﻣﻲ ﮐﻨﺪ ﮐﻪ ﻧﺤﻮﻩ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ ﺑﻬﻴﻨﻪ ﺑﺮﺍﻱ ﺍﻧﻮﺍﻉ‬
‫ﺳﺮﻭﻳﺲ ﻫﺎ ﭼﻴﺴﺖ؟ ﺑﻮﺿﻮﺡ ﻧﺤﻮﻩ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ ﺭﻭﻱ ﺳﺮﻭﻳﺲ ﻫﺎ ﻭ ﻣﻨﺎﻳﻊ ﺷﺒﮑﻪ ﺭﻭﻱ ﺍﻧﺘﺨﺎﺏ ﮐﺎﺭﺑﺮﺍﻥ ﻭ ﺩﺭ ﻧﺘﻴﺠﻪ ﺭﻭﻱ ﮐﺎﺭﺍﻳﻲ ﺷﺒﮑﻪ‬
‫ﺗﺎﺛﻴﺮ ﻣﺴﺘﻘﻴﻢ ﺧﻮﺍﻫﺪ ﺩﺍﺷﺖ‪.‬‬
‫ﺑﺮﺍﻱ ﺑﺮﺭﺳﻲ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺭﺍ ﮐﺎﺭﺑﺮﺍﻥ ﺷﺒﮑﻪ ﻭ ﻣﺪﻳﺮ ﺩﺭ ﻧﻈﺮ ﻣﻲ ﮔﻴﺮﻳﻢ ﮐﻪ ﭘﺲ ﺍﺯ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ ﺳﺮﻭﻳﺲ ﻫﺎ ﺗﻮﺳﻂ ﻣﺪﻳﺮ ﺷﺒﮑﻪ‪،‬‬
‫ﻫﺮﻳﮏ ﺍﺯ ﮐﺎﺭﺑﺮﺍﻥ ﺑﻄﻮﺭ ﻣﺴﺘﻘﻞ ﻧﻮﻋﻲ ﺍﺯ ﺳﺮﻭﻳﺲ ﺷﺒﮑﻪ ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﮐﻨﺪ‪ .‬ﺣﺎﻝ ﺳﻮﺩ ﻫﺮﻳﮏ ﺍﺯ ﮐﺎﺭﺑﺮﺍﻥ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ ﺑﺮﺍﺑﺮ ﺍﺧﺘﻼﻑ‬
‫ﺍﺭﺯﺵ ﻭﺍﻗﻌﻲ ﺳﺮﻭﻳﺲ ﺍﻧﺘﺨﺎﺑﻲ ﺩﺭ ﻧﻈﺮ ﮐﺎﺭﺑﺮ ﻭ ﻗﻴﻤﺖ ﭘﺮﺩﺍﺧﺖ ﺷﺪﻩ ﺑﺎﺑﺖ ﺁﻥ ﺳﺮﻭﻳﺲ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ‪ .‬ﺗﺎﺑﻊ ﺳﻮﺩ ﻣﺪﻳﺮ ﺷﺒﮑﻪ ﺭﺍ ﻣﻲ ﺗﻮﺍﻥ‬
‫ﻭﺍﺑﺴﺘﻪ ﺑﻪ ﮐﺎﺭﺍﻳﻲ ﺷﺒﮑﻪ ﻭ ﻳﺎ ﺭﺿﺎﻳﺖ ﮐﺎﺭﺑﺮﺍﻥ ﺍﺯ ﻗﻴﻤﺖ ﮔﺬﺍﺭﻱ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻫﺰﻳﻨﻪ ﻫﺎ ﻭ ﺳﻮﺩ ﻻﺯﻡ ﺑﺮﺍﻱ ﻣﺪﻳﺮﺍﻥ ﺷﺒﮑﻪ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ‪.‬‬
‫ﺑﺮﺍﻱ ﻣﻄﺎﻟﻌﻪ ﺑﻴﺸﺘﺮ ﺑﻪ ﻣﺮﺟﻊ ]‪ [6‬ﺭﺟﻮﻉ ﮐﻨﻴﺪ‪.‬‬
‫‪ -3-5‬ﺑﺎﺯﻱ ﻣﺪﻳﺮﻳﺖ ﺍﻋﺘﺒﺎﺭ ﺩﺭ ﺷﺒﮑﻪ‬
‫ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻳﻲ ﮐﻪ ﻫﻤﮑﺎﺭﻱ ﻣﺘﻘﺎﺑﻞ ﮔﺮﻩ ﻫﺎ ﺩﺭ ﺍﻧﺠﺎﻡ ﺳﺮﻭﻳﺲ ﺑﺮﺍﻱ ﺳﺎﻳﺮ ﮔﺮﻩ ﻫﺎ ﻻﺯﻡ ﺍﺳﺖ‪ ،‬ﺷﻨﺎﺳﺎﻳﻲ ﮔﺮﻩ ﻫﺎﻱ ﻫﻤﮑﺎﺭ ﺩﺭ ﺷﺒﮑﻪ ﺍﺯ‬
‫ﮔﺮﻩ ﻫﺎﻱ ﺧﻮﺩﺧﻮﺍﻩ ﺍﻣﺮﻱ ﺿﺮﻭﺭﻱ ﺍﺳﺖ‪ .‬ﻧﻤﻮﻧﻪ ﺑﺎﺭﺯ ﺍﻳﻦ ﺷﺒﮑﻪ ﺷﺒﮑﻪ ﻫﺎﻱ ﻫﻤﻪ ﺟﺎﻳﻲ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺎ ﻣﺴﻴﺮ ﻳﺎﺏ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﻤﺎﻥ‬
‫ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺴﺘﻨﺪ‪ .‬ﻧﻤﻮﻧﻪ ﻣﻬﻢ ﺩﻳﮕﺮ‪ ،‬ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﻈﻴﺮ ﺑﻪ ﻧﻈﻴﺮ ﻫﺴﺘﻨﺪ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺎ ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺷﺒﮑﻪ ﺑﻪ ﻣﻌﻨﻲ ﺑﻪ ﺍﺷﺘﺮﺍﮎ‬
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‫ﮔﺬﺍﺷﺘﻦ ﻓﺎﻳﻞ ﻫﺎ ﻭ ﺩﻳﮕﺮ ﻣﻨﺎﺑﻊ ﺑﺎ ﺳﺎﻳﺮ ﮔﺮﻩ ﻫﺎﺳﺖ‪ .‬ﻭ ﻳﺎ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﺷﺒﮑﻪ ﻫﺎﻱ ﭘﺮﺩﺍﺯﺵ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﺷﺎﺭﻩ ﮐﺮﺩ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺎ ﻫﻤﮑﺎﺭﻱ‬
‫ﺑﻪ ﻣﻌﻨﻲ ﺑﻪ ﺍﺷﺘﺮﺍﮎ ﮔﺬﺍﺷﺘﻦ ﻗﺪﺭﺕ ﭘﺮﺩﺍﺯﺵ‪ ،‬ﺩﺭ ﺯﻣﺎﻥ ﺑﻴﮑﺎﺭﻱ ﭘﺮﺩﺍﺯﻧﺪﻩ ﻫﺎﺳﺖ‪.‬‬
‫ﺩﺭ ﺍﻳﻦ ﺷﺒﮑﻪ ﻫﺎ ﺑﺎﻳﺪ ﺗﺪﺍﺑﻴﺮﻱ ﺑﺮﺍﻱ ﺍﻳﺠﺎﺩ ﺍﻧﮕﻴﺰﻩ ﻫﻤﮑﺎﺭﻱ ﻣﻴﺎﻥ ﮔﺮﻩ ﻫﺎ ﺍﻧﺪﻳﺸﻴﺪﻩ ﺷﻮﺩ‪ .‬ﻳﮑﻲ ﺍﺯ ﺭﺍﻩ ﮐﺎﺭﻫﺎﻱ ﭘﻴﺸﻨﻬﺎﺩﻱ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺑﻪ‬
‫ﻫﺮﻳﮏ ﺍﺯ ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﭘﺎﺭﺍﻣﺘﺮﻱ ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﻌﻴﺎﺭ ﺍﻋﺘﺒﺎﺭ ﺩﺭ ﺷﺒﮑﻪ ﺗﻌﻠﻖ ﻳﺎﺑﺪ ﻭ ﺍﻭﻟﻮﻳﺖ ﻫﺮ ﮔﺮﻩ ﺩﺭ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻨﺎﺑﻊ ﺷﺒﮑﻪ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ‬
‫ﻣﻴﺰﺍﻥ ﺍﻋﺘﺒﺎﺭﺵ ﺗﻌﻴﻴﻦ ﺷﻮﺩ‪ .‬ﺑﺪﻳﻦ ﺗﺮﺗﻴﺐ ﮔﺮﻩ ﻫﺎﻱ ﺧﻮﺩﺧﻮﺍﻩ ﺑﻪ ﺗﺪﺭﻳﺞ ﺍﺯ ﺷﺒﮑﻪ ﺣﺬﻑ ﺧﻮﺍﻫﻨﺪ ﺷﺪ‪.‬‬
‫ﺍﻣﺎ ﻧﮑﺘﻪ ﺩﻳﮕﺮ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺷﺒﮑﻪ ﻫﺰﻳﻨﻪ ﻫﺎﻳﻲ ﺑﺮﺍﻱ ﮔﺮﻩ ﻫﺎ ﺩﺭ ﺑﺮﺩﺍﺭﺩ‪ .‬ﻣﺜﻼ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ ‪ ،‬ﺗﻮﺍﻥ ﺍﺗﻼﻓﻲ ﺑﺮﺍﻱ‬
‫ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺑﺴﺘﻪ ﻫﺎﻱ ﺳﺎﻳﺮ ﮔﺮﻩ ﻫﺎ ﻫﺰﻳﻨﻪ ﺍﻱ ﻏﻴﺮ ﻗﺎﺑﻞ ﺻﺮﻑ ﻧﻈﺮ ﮐﺮﺩﻥ ﺍﺳﺖ‪ .‬ﻭ ﻳﺎ ﻣﻲ ﺗﻮﺍﻥ ﺑﻪ ﻫﺰﻳﻨﻪ ﻣﺸﻐﻮﻝ ﻣﺎﻧﺪﻥ ﭘﺮﺩﺍﺯﻧﺪﻩ ﺩﺭ‬
‫ﺷﺒﮑﻪ ﻫﺎﻱ ﭘﺮﺩﺍﺯﺵ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﺷﺎﺭﻩ ﮐﺮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﻃﺒﻴﻌﻲ ﺍﺳﺖ ﮐﻪ ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﺑﻪ ﺩﻧﺒﺎﻝ ﻣﺼﺎﻟﺤﻪ ﺍﻱ ﺑﻴﻦ ﭘﺎﺭﺍﻣﺘﺮ ﺍﻋﺘﺒﺎﺭ ﺩﺭ‬
‫ﺷﺒﮑﻪ ﻭ ﮐﺎﻫﺶ ﻫﺰﻳﻨﻪ ﻧﺎﺷﻲ ﺍﺯ ﻫﻤﮑﺎﺭﻱ ﺩﺭ ﺷﺒﮑﻪ ﺑﺎﺷﻨﺪ‪ .‬ﺑﺎ ﺍﻳﻦ ﺍﻭﺻﺎﻑ‪ ،‬ﺑﺮﺭﺳﻲ ﻭ ﻣﺪﻝ ﺳﺎﺯﻱ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﺑﺎﺯﻱ‪ ،‬ﭼﻨﺪﺍﻥ‬
‫ﺩﻭﺭ ﺍﺯ ﺍﻧﺘﻈﺎﺭ ﻧﻴﺴﺖ‪.‬‬
‫‪ -4-5‬ﺑﺎﺯﻱ ﮐﻨﺘﺮﻝ ﺟﺮﻳﺎﻥ ﺩﺭ ﺷﺒﮑﻪ‬
‫ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﻣﻲ ﺩﺍﻧﻴﺪ ﮐﻨﺘﺮﻝ ﺍﻧﺒﺎﺷﺘﮕﻲ ﻳﮑﻲ ﺍﺯ ﻣﻬﻤﺘﺮﻳﻦ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﺷﺒﮑﻪ ﻫﺎﻱ ﺩﻳﺘﺎﮔﺮﺍﻡ ﺩﺭ ﻻﻳﻪ ﺍﻧﺘﻘﺎﻝ ﺩﺍﺩﻩ ﺍﺳﺖ ﮐﻪ ﻃﺒﻖ ﺁﻥ‬
‫ﮐﺎﺭﺑﺮﺍﻥ ﻣﻮﻇﻒ ﺑﻪ ﻣﺤﺪﻭﺩ ﻧﮕﻪ ﺩﺍﺷﺘﻦ ﻧﺮﺥ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﺑﻪ ﺩﺍﺧﻞ ﺷﺒﮑﻪ ﻣﻲ ﺷﻮﻧﺪ‪ ،‬ﺯﻳﺮﺍ ﺩﺭ ﻏﻴﺮ ﺍﻳﻦ ﺻﻮﺭﺕ ﺑﻪ ﻋﻠﺖ‬
‫ﮔﺮﻓﺘﮕﻲ ﻭ ﺗﺎﺧﻴﺮ‪ ،‬ﮐﺎﺭﺍﻳﻲ ﺷﺒﮑﻪ ﺑﺸﺪﺕ ﮐﺎﻫﺶ ﺧﻮﺍﻫﺪ ﻳﺎﻓﺖ‪ .‬ﺍﻣﺎ ﺳﻮﺍﻝ ﻣﻬﻢ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺁﻳﺎ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ ﻭ ﺑﺎ ﮔﺮﻩ ﻫﺎﻱ‬
‫ﺧﻮﺩﺧﻮﺍﻩ‪ ،‬ﻧﺮﺥ ﻭﺭﻭﺩ ﺑﺴﺘﻪ ﺑﻪ ﺷﺒﮑﻪ ﻣﺤﺪﻭﺩ ﻣﻲ ﻣﺎﻧﺪ ﻳﺎ ﻧﻪ؟‬
‫ﺑﺮﺍﻱ ﺑﺮﺭﺳﻲ ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﻣﻲ ﺗﻮﺍﻥ ﮔﺮﻩ ﻫﺎﻱ ﺷﺒﮑﻪ ﺭﺍ ﺑﻪ ﻋﻨﻮﺍﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺎﺯﻱ ﮐﻨﺘﺮﻝ ﺍﻧﺒﺎﺷﺘﮕﻲ ﺩﺭ ﺷﺒﮑﻪ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ ﮐﻪ ﻫﺮﻳﮏ ﻣﻲ‬
‫ﺗﻮﺍﻧﻨﺪ ﻧﺮﺥ ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎﻱ ﺩﺍﺩﻩ ﺧﻮﺩ ﺑﻪ ﺷﺒﮑﻪ ﺭﺍ ﮐﻨﺘﺮﻝ ﮐﻨﻨﺪ‪ .‬ﺗﺎﺑﻊ ﺳﻮﺩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺑﺮﺍﻱ ﻓﺮﺳﺘﻨﺪﻩ ﻫﺎ ﺩﺭ ﺍﻳﻦ ﺑﺎﺯﻱ ﺑﺎﻳﺪ ﺑﺎ‬
‫ﻧﺮﺥ ﺍﺭﺳﺎﻝ ﺩﺍﺩﻩ ﺑﻪ ﺷﺒﮑﻪ ﺭﺍﺑﻄﻪ ﻣﺴﺘﻘﻴﻢ ﻭﻟﻲ ﺑﺎ ﺗﺎﺧﻴﺮ ﺑﺴﺘﻪ ﻫﺎ ﺩﺭ ﺷﺒﮑﻪ ﻧﺴﺒﺖ ﻋﮑﺲ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﻣﺴﺎﻟﻪ ﺑﻪ ﻃﻮﺭ ﺟﺰﺋﻲ ﺗﺮ ﺩﺭ‬
‫ﻣﺮﺟﻊ ]‪ [9‬ﺑﺮﺭﺳﻲ ﻭ ﺗﻌﺎﺩﻝ ﻧﺶ ﺑﺎﺯﻱ ﺑﺎ ﻓﺮﺽ ﻫﺎﻱ ﻗﺎﺑﻞ ﻗﺒﻮﻟﻲ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬
‫‪ -6‬ﻧﺘﻴﺠﻪ ﮔﻴﺮﻱ‬
‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ ﺑﻴﺎﻥ ﻣﺜﺎﻝ ﻫﺎﻱ ﻣﺘﻌﺪﺩ‪ ،‬ﺍﻳﺪﻩ ﻣﺪﻝ ﺳﺎﺯﻱ ﻣﺴﺎﺋﻠﻲ ﺍﺯ ﻻﻳﻪ ﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺷﺒﮑﻪ ﺑﻪ ﮐﻤﮏ ﻧﻈﺮﻳﻪ ﺑﺎﺯﻱ ﺭﺍ ﺑﻴﺎﻥ ﮐﺮﺩﻳﻢ ﻭ‬
‫ﻧﺸﺎﻥ ﺩﺍﺩﻳﻢ ﮐﻪ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ ﻧﻘﺎﻁ ﺗﻌﺎﺩﻝ ﺑﺎﺯﻱ ﻫﺎﻱ ﺷﺒﮑﻪ ﭼﮕﻮﻧﻪ ﻣﻲ ﺗﻮﺍﻧﺪ ﺩﺭ ﻃﺮﺍﺣﻲ ﭘﺮﻭﺗﮑﻞ ﻫﺎﻱ ﻣﻘﺎﻭﻡ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﺎﻣﺘﻤﺮﮐﺰ‬
‫ﮐﻪ ﺑﻪ ﺳﺮﻋﺖ ﺩﺭ ﺣﺎﻝ ﺗﻮﺳﻌﻪ ﻫﺴﺘﻨﺪ ﻣﺎﻧﻨﺪ ﺷﺒﮑﻪ ﻫﺎﻱ ﺑﻲ ﺳﻴﻢ‪ ،‬ﻫﻤﻪ ﺟﺎﻳﻲ‪ ،‬ﭘﺮﺩﺍﺯﺵ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻭ ﺷﺒﮑﻪ ﻫﺎﻱ ﻧﻈﻴﺮ ﺑﻪ ﻧﻈﻴﺮ ﺑﻪ ﮐﺎﺭ‬
‫ﺭﻭﺩ‪ .‬ﺑﻪ ﻫﺮ ﺣﺎﻝ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺗﺤﻘﻴﻘﺎﺕ ﺟﺪﻳﺪ ﺑﻮﺩﻩ ﻭ ﻫﻨﻮﺯ ﻣﺴﺎﺋﻞ ﺑﺎﺯ ﻭ ﺣﻞ ﻧﺸﺪﻩ ﺯﻳﺎﺩﻱ ﺩﺭ ﺁﻥ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪.‬‬
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‫ ﻣﺮﺍﺟﻊ‬-7
[1] Allen MacKenzie and Luiz DaSilva, Game Theory for Wireless Engineers, Morgan &
Claypool Publishers, 2006.
[2] Webb, James N, Game Theory Decisions, Interaction and Evolution Series: Springer
Undergraduate Mathematics Series, 2007
[3] D. Goodman and N. Mandayam, “Power control for wireless data,” IEEE Pers.
Communications Magazine, vol. 7, no. 2, pp. 48–54, April 2000.
[4] Allen MacKenzie and Stephen Wicker, “Game Theory and the Design of Self-Configuring
Adaptive Wireless Networks”, IEEE Commun. Mag., pp. 126, Nov. 2001
[5] Webb, James N, Game Theory Decisions, Interaction and Evolution Series: Springer
Undergraduate Mathematics Series, 2007
[6] L. A. DaSilva, “Static pricing inmultiple-service networks: A game-theoretic
approach,” Ph. D. dissertation, the University of Kansas, 1998.
[7] L. A. DaSilva and V. Srivastava, “Node participation in ad-hoc and peer-to-peer
networks: A game-theoretic formulation,” in Workshop on Games and Emergent
Behaviorin Distributed Computing Environments, Birmingham, U K, September 2004.
[8] Mark Felegyhazi, Jean-Pierre Hubaux, “Game Theory in Wireless Networks: A Tutorial”,
2006, EPLF university.
[9] Y. A. Korilis and A. A. Lazar, “On the existence of equilibria in noncooperative optimal
flow control,” J. ACM, 1995.
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