有价证券竞价：风险规避与正相关
On Bidding with Securities: Risk Aversion and Positive Dependence
摘要：
DeMarzo et al.（2005）考虑了从一个完全有序的证券家族中选择投标的拍卖，这些证券的价值与被拍卖的资源有关。本文定义了一个概念的相对陡峭的家庭的证券，并表明，陡峭的家庭提供更大的预期收入的卖方。两个假设是：购买者是风险中性的，通过购买者的价值和信号实现的随机变量是关联的。我们表明，这种收入排名持有的第二价格拍卖的情况下，风险规避。然而，它不成立，如果从属关系是放松到一个较少的限制性形式的正相关，即一阶随机优势（FOSD）。我们定义了证券族的相对强陡度，并证明了它为FOSD情形下比较两个证券族提供了一个充分必要条件。所有结果都延伸到英国拍卖。
英文摘要：
DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk-neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk-aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.
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