472 research outputs found
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
The derived category of quasi-coherent sheaves and axiomatic stable homotopy
We prove in this paper that for a quasi-compact and semi-separated (non
necessarily noetherian) scheme X, the derived category of quasi-coherent
sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of
Hovey, Palmieri and Strickland, answering a question posed by Strickland.
Moreover we show that it is unital and algebraic. We also prove that for a
noetherian semi-separated formal scheme X, its derived category of sheaves of
modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy
category. It is algebraic but if the formal scheme is not a usual scheme, it is
not unital, therefore its abstract nature differs essentially from that of the
derived category of a usual scheme.Comment: v2: 31 pages, some improvements in exposition; v3 updated
bibliography, to appear Adv. Mat
Simple, optimal and efficient auctions
Proceedings of the 7th International Workshop, WINE 2011, Singapore, December 11-14, 2011.We study the extent to which simple auctions can simultaneously achieve good revenue and efficiency guarantees in single-item settings. Motivated by the optimality of the second price auction with monopoly reserves when the bidders’ values are drawn i.i.d. from regular distributions [12], and its approximate optimality when they are drawn from independent regular distributions [11], we focus our attention to the second price auction with general (not necessarily monopoly) reserve prices, arguably one of the simplest and most intuitive auction formats. As our main result, we show that for a carefully chosen set of reserve prices this auction guarantees at least 20% of both the optimal welfare and the optimal revenue, when the bidders’ values are distributed according to independent, not necessarily identical, regular distributions. We also prove a similar guarantee, when the values are drawn i.i.d. from a—possibly irregular—distribution.National Science Foundation (U.S.) (award CCF-0953960)National Science Foundation (U.S.) (CCF-1101491
Gorenstein homological algebra and universal coefficient theorems
We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories
On the existence of a compact generator on the derived category of a noetherian formal scheme
In this paper, we prove that for a noetherian formal scheme X, its derived
category of sheaves of modules with quasi-coherent torsion homologies D_qct(X)
is generated by a single compact object. In an appendix we prove that the
category of compact objects in D_qct(X) is skeletally small.Comment: 13 page
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