How (not) to raise money

We show that standard winner-pay auctions are inept fund-raising mechanisms because of the positive externality bidders forgo if they top another's high bid. Revenues are suppressed as a result and remain finite even when bidders value a dollar donated the same as a dollar kept. This problem does not occur in lotteries and all-pay auctions, where bidders pay irrespective of whether they win. We introduce a general class of all-pay auctions, rank their revenues, and illustrate how they dominate lotteries and winner-pay formats. The optimal fund-raising mechanism is an all-pay auction augmented with an entry fee and reserve price

Incommensurate interactions and non-conventional spin-Peierls transition in TiOBr

Temperature-dependent x-ray diffraction of the low-dimensional spin 1/2 quantum magnet TiOBr shows that the phase transition at T_{c2} = 47.1 (4) K corresponds to the development of an incommensurate superstructure. Below T_{c1} = 26.8 \pm 0.3 K the incommensurate modulation locks in into a two-fold superstructure similar to the low-temperature spin-Peierls state of TiOCl. Frustration between intra- and interchain interations within the spin-Peierls scenario, and competition between two-dimensional magnetic order and one-dimensional spin-Peierls order are discussed as possible sources of the incommensurability.Comment: 5 pages including 3 figures and 1 tabl