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

Brane Cosmic String Compactification in Brans-Dicke Theory

We investigate an alternative compactification of extra dimensions using local cosmic string in the Brans-Dicke gravity framework. In the context of dynamical systems it is possible to show that there exist a stable field configuration for the Einstein-Brans-Dicke equations. We explore the analogies between this particular model and the Randall-Sundrum scenario.Comment: RevTex, 5 pages, no figures. To appear in the Physical Review

Towards an hybrid compactification with a scalar-tensor global cosmic string

We derive a solution of the gravitational equations which leads to a braneworld scenario in six dimensions using a global cosmic string solution in a low energy effective string theory framework. The final spacetime is composed by one warped brane with $\mathbb{R}^{(3,1)}\times S^{1}$ topology and a power law warp factor, and one noncompact extra dimension transverse to the brane. By looking at the current experimental bounds, we find a range of parameters in which, if the on-brane dimension has an acceptable size, it does not solve the hierarchy problem. In another example this problem is smoothed by the Brans-Dicke parameter.Comment: RevTex, 7 pages. New version to be published in the JCAP (2008