Computer Science – Computer Science and Game Theory
Scientific paper
2011-11-06
Computer Science
Computer Science and Game Theory
16 pages, 3 figures. This is a work in progress
Scientific paper
DeMarzo et al. (2005) considers auctions in which bids are selected from a completely ordered family of securities whose ultimate 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 a higher expected revenue to the seller. Two key assumptions are: (i) the buyers are risk-neutral; (ii) the random variables through which values and signals of the buyers are realized are affiliated. This paper studies the role of these assumptions and the consequences of relaxing them in the case of the second price auction. We show that the revenue ranking of families of securities of DeMarzo et al. (2005) holds for risk averse buyers. However, this ranking is not preserved if affiliation is relaxed to a less restrictive form of positive dependence among values and signals, namely, first order stochastic dominance. We then define the relative strong steepness of families of securities and show that a strongly steeper family generates a higher expected revenue for the seller in the case of this more general form of positive dependence.
Abhishek Vineet
Hajek Bruce
Williams Steven R.
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