※ 引述《qqqqqwer (qqqqqwer)》之铭言： : 今天在整理以前的东西的时候 : 翻到了以前的赛局理论考卷 : 这一题让我在考试的时候想了很久 : 最後还是放弃做答了 : 不知道板上的强者是否可以为我说明一下 : 这一题到底该怎麽解??? : 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? : 我那时候只有想到一个很基本的观念 : 就是如果今天有A和B两个人 假设其它条件相同 : 则店家会把店开在A和B的中点 : 但是这题是两个不同的地点 且有代数字下去算 : 不知道我想到的那个观念可不可以套进来应用?? 我的想法是 所有厂商同时选择downtown 或 suburbs 那麽最後均衡应该发生在座落於downtown 与座落於suburbs的利润相等 由於全部共有10家厂商 座落於downtown有n家 那麽座落於subsurbs则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必不为-2 所以downtown有6家 subsurbs有4家（10-6） 而每家厂商的利润为5*6-6*6+50＝48-4＝44 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 218.169.50.2