※ 引述《qqqqqwer (qqqqqwer)》之銘言： : 今天在整理以前的東西的時候 : 翻到了以前的賽局理論考卷 : 這一題讓我在考試的時候想了很久 : 最後還是放棄做答了 : 不知道板上的強者是否可以為我說明一下 : 這一題到底該怎麼解??? : Consider a market with 10 firms. Simultaneously and independently, the firms : choose between locating downtown and locating in the suburbs. : The profit of each firm is influenced by the number of other firms : that locate in the same area. Specifically, the profit of a firm that locates : downtown is given by 5n – n2 + 50, where n denotes the number of firms that : locate downtown . Similarly, the profit of a firm that locates in the : suburbs is given by 48 – m, where m denotes the number of firms that locate : in the suburbs. In equilibrium, how many firms locate in each region and : what is the profit of each? : 我那時候只有想到一個很基本的觀念 : 就是如果今天有A和B兩個人 假設其它條件相同 : 則店家會把店開在A和B的中點 : 但是這題是兩個不同的地點 且有代數字下去算 : 不知道我想到的那個觀念可不可以套進來應用?? 我的想法是 所有廠商同時選擇downtown 或 suburbs 那麼最後均衡應該發生在座落於downtown 與座落於suburbs的利潤相等 由於全部共有10家廠商 座落於downtown有n家 那麼座落於subsurbs則10-n家（m） 故可知 5n-n2+50=48-(10-n) =>n2-4n-12=0 =>(n-6)(n+2)=0 故n=6 or-2 又n必不為-2 所以downtown有6家 subsurbs有4家（10-6） 而每家廠商的利潤為5*6-6*6+50＝48-4＝44 --

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