Nas–Walras equilibria of a large economy

Individuals exchange contracts for the delivery of commodities in competitive markets and, simultaneously, act strategically; actions affect utilities across individuals directly or through the payoffs of contracts. This encompasses economies with asymmetric information. Nash–Walras equilibria exist for large economies, even if utility functions are not quasi-concave and choice sets are not convex, which is the case in standard settings; the separation of the purchase from the sale of contracts and the pooling of the deliveries on contracts guarantee that the markets for commodities clear.

MLL, a mammalian trithorax-group gene, functions as a transcriptional maintenance factor in morphogenesis

Determinative events in vertebrate embryogenesis appear to require the continuous expression of spatial regulators such as the clustered homeobox genes. The mechanisms that govern long-term patterns of gene expression are not well understood. In Drosophila, active and silent states of developmentally regulated loci are maintained by trithorax and Polycomb group. We have examined the developmental role of a mammalian homolog of trx and putative oncogene, Mll. Knockout mice reveal that Mll is required for maintenance of gene expression early in embryogenesis. Downstream targets of Mll including Hoxa7 are activated appropriately in the absence of Mll but require Mll for sustaining their expression. The Mll−/− phenotype manifests later in development and is characterized by branchial arch dysplasia and aberrant segmental boundaries of spinal ganglia and somites. Thus, Mll represents an essential mechanism of transcriptional maintenance in mammalian development, which functions in multiple morphogenetic processes.