Sealed bid second price auctions with discrete bids

A single item is sold to two bidders by way of a sealed bid second price auction in which bids are restricted to a set of discrete values. Restricting attention to symmetric pure strategy behavior on the part of bidders, a unique equilibrium exists. When following these equilibrium strategies bidders may bid strictly above or below their valuation, implying that the item may be awarded to a bidder other than the high valuation bidder. In an auction with two acceptable bids, the expected revenue of the seller may be maximized by a high bid level not equal to the highest possible bidder valuation and may exceed the expected revenue from an analogous second price auction with continuous bidding (and no reserve price). With three acceptable bids, a revenue maximizing seller may choose unevenly spaced bids. With an arbitrary number of evenly spaced bids, as the number of acceptable bids is increased, the expected revenue of the seller and the probability of ex post inefficiency both may either increase or decrease

Galactic exploration by directed Self-Replicating Probes, and its implications for the Fermi paradox

This paper proposes a long term scheme for robotic exploration of the galaxy,and then considers the implications in terms of the `Fermi paradox' and our search for ETI. We discuss the parameter space of the `galactic ecology' of civilizations in terms of the parameters T (time between ET civilizations arising) and L, the lifetime of these civilizations. Six different regions are described.Comment: 1 figur

Determining Shared Working Memory Systems for Rhythmic Incongruities in Music and Language using functional Near-Infrared Spectroscopy

Rhythmic organization of auditory information is used differently in the retention of music and spoken language. However, similar areas of the prefrontal cortex (PFC) have been implicated in the retention of unusual rhythmic patterns. This study investigated the degree of PFC activation using functional near-infrared spectroscopy (fNIRS) during three rhythmic pattern manipulation working memory tasks. In addition the normalized pair-wise variability index (NPVI) was tested as a measure of rhythmic accuracy. Of the six participants considered, three demonstrated greater activation of the right PFC in response to the Rhythmic Motor task, a manipulation of musical rhythms. Similar activation was observed for the Stress Speech task, which altered stress patterns in natural speech. No changes in activation were observed in the Rhythmic Speech task, which paired speech with metric patterns. The NPVI values did not reflect task performance. Refinement is needed to determine if the current procedure accurately measures rhythmic working memory

Enhanced Heavy-Element Formation in Baryon-Inhomogeneous Big-Bang Models

We show that primordial nucleosynthesis in baryon inhomogeneous big-bang models can lead to significant heavy-element production while still satisfying all the light-element abundance constraints including the low lithium abundance observed in population II stars. The parameters which admit this solution arise naturally from the process of neutrino induced inflation of baryon inhomogeneities prior to the epoch of nucleosynthesis. These solutions entail a small fraction of baryons (\le 2\%) in very high density regions with local baryon-to-photon ratio $\eta^h\approx 10^{-4}$, while most baryons are at a baryon-to-photon ratio which optimizes the agreement with light-element abundances. The model would imply a unique signature of baryon inhomogeneities in the early universe, evidenced by the existence of primordial material containing heavy-element products of proton and alpha- burning reactions with an abundance of $[Z]\sim -6 to -4$.Comment: 19 pages in plain Tex, 5 figures (not included) available by fax or mail upon request, ApJ in press, L