[求助] 一个second price, affiliated value auction的问题

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我正在做一个paper，其中涉及到一个问题，很难。不知大家有没有人知道。
有两个second price auctions。In the first auction，n bidders draw valuations from distribution of random variable X. In the other, bidders draw from Y. Valuations are affiliated. Now we know the expected difference between the first two order statistics of X is smaller than that of Y. The question is that under what conditions we can say that the winning bidder's expected profit is higher in the second auction.
当然如果是independent value auctions那么这个问题就很简单了。

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关键词：affiliated Affiliate auction Second secon value Price Second auction affiliated

这个问题一句话说不清的，建议你读这篇论文：
A Theory of Auctions and Competitive Bidding

Econometrica 1982

Paul R. Milgrom; Robert J. Weber

谢谢建议。不过这篇文章是研究auction必读啊，我很早以前读过了。

这个问题很难，现有的论文、书籍上没有答案。Milgrom and Weber 82研究了affilated value auction，但并没有涉及到两个auction的比较。假设说In the symmetric affiliated-value model, a bidder observing signal Wi has value U(Wi, {Wj}，j<>i). Bidder i’s bid function is b(w) = E(U|Wi = w,Wm = w), where Wm is the maximum value among the other bidders. The winner’s expected profit is  EU(W(1), {W(j)}, (j)<>(1)) − E(b(W(2))), where W(1),...,W(n) are order statistics in decreasing order.

接下来就得比较两个auction的winner expected profit了。但这里涉及到conditional probability，怎么比呢？


2# pppjw

哈哈，这个就要我倡导的拍卖仿真计算了。我猜随机占优关系应该会是一个判断标准。我可以有办法给出数值仿真实验的结论。不过我现在忙不过来，等我空了再就你这个问题做做计算机仿真实验。

多谢。不过不麻烦了，我做过很多仿真，没有发现可以用的condition。