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一项工程招标,规则是投标者各自将投标价格写下来放到信封里,最后出价低的中标.招标方按其出价与其签工程承包合同.如果出价相同,则抛硬币决定中标者.假定只有两个投标者.招标方不知道他们的实际成本,但知道他们的实际成本以相等的概率为H,M,L, (H>M>L). 投标者知道自己的实际成本但不知道其他投标者的成本.并且当投标者实际成本为L时,会出价M, 实际成本为H或M时则出价H.假定投标者之间没有共谋, 问招标者的期望签约价格为多少?

我的答案是: M(5/9)+H(4/9 ) 但答案是H(2/3)+M(1/3)

哪位能指点一下?谢了.

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关键词：工程承包 承包合同 不知道 签约价 中标者 概率

答案对了，设两个公司为Ｘ，Ｙ，他们出价Ｈ或者Ｍ，对应概率为Ｐ（Ｈ，Ｈ）＝４／９　Ｐ（Ｈ，Ｍ）＝２／９　Ｐ（Ｍ，Ｈ）＝２／９　Ｐ（Ｍ，Ｍ）＝１／９　去底价者的价格，所以取Ｍ的概率为２／９+２／９+１／９＝５／９　取Ｈ的概率为４／９，所以Ｅ（Ｘ，Ｙ）＝M(5/9)+H(4/9 )

楼上的，你的解法中没有考虑投硬币的过程。

以下是引用nick0895在2005-12-8 19:55:50的发言：

答案对了，设两个公司为Ｘ，Ｙ，他们出价Ｈ或者Ｍ，对应概率为Ｐ（Ｈ，Ｈ）＝４／９　Ｐ（Ｈ，Ｍ）＝２／９　Ｐ（Ｍ，Ｈ）＝２／９　Ｐ（Ｍ，Ｍ）＝１／９　去底价者的价格，所以取Ｍ的概率为２／９+２／９+１／９＝５／９　取Ｈ的概率为４／９，所以Ｅ（Ｘ，Ｙ）＝M(5/9)+H(4/9 )

你也是认为我作对了而答案是错的吧.

签约价格不是M就会是H.只要至少有一个投标者的实际成本为L,签约价格就会是M. 所以当投标者成本都不是L,签约价格就是H.而都不是L的概率是4/9. 因此至少有一个是L的概率为5/9.

所以期望=5M/9+4H/9

抛硬币只影响中标者,而不影响中标价格.

General Scooters has decided to replace its old assembly line with a new one that makes extensive use of robots. There are two contractors who would be able to build the new assembly line. General Scooters's industrial spies and engineers have done some exploratory researchof their own on the costs of building the new assembly line for each of the two contractors. They have discovered that for each of them, this cost will take one of three possible values H, M, and L, where H >M > L.

Unfortunately, General Scooters has not been able to determine whether the costs of either of the bidders are H, M, or L. The best information that General Scooters's investigators have been able to give it is that for each contractor the probability is 1/3 that the cost is H, 1/3 that the cost is M, and 1/3 that the cost is L and that the probability distribution of costs is independent between the two contractors. Each contractor knows its own costs but thinks that the other's costs are equally likely to be H, M, or L. General Scooters is confident that the contractors will not collude.

General Scoooters accept sealed bids from the two contractors for constructing the assembly line and that it announce that it will award the contract to the low bidder and will pay the low bidder the amount bid by her.

Suppose a contractor will bid M if her costs are L, and she will bid H if her costs are H or M. If contractors use this strategy, what is the expected cost of the project to General Scooters?

这是原题