Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

High-resolution physical mapping by combined Alu-hybridization/PCR screening: construction of a yeast artificial chromosome map covering 31 centimorgans in 3p21-p14.

We describe an integrated approach to large-scale physical mapping using an Alu-PCR hybridization screening strategy in conjunction with direct PCR-based screening to construct a continuous yeast artificial chromosome map covering >20 mb in human chromosome 3, bands p14-p21, composed of 205 loci, connected by 480 yeast artificial chromosomes, with average interlocus distance of approximately equal to 100 kb. We observe an inverse distribution of Alu-PCR and (CA)n markers. These results suggest that the two screening methods may be complementary and demonstrate the utility of Alu-PCR hybridization screening in the closure of high-resolution human physical maps.