/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

/pdf/the-theory-of-industrial-organization-19bejph0ej.pdf

The Theory of Industrial Organization

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

Hundreds of variants clustered in genomic loci and biological pathways affect human height

A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice plans result in appeals by unsatisfied parents. We formulate the school choice problem as a mechanism design problem and analyze some of the existing school choice plans including those in Boston, Columbus, Minneapolis, and Seattle. We show that these existing plans have serious shortcomings, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues.

/pdf/school-choice-a-mechanism-design-approach-11t5vq18ed.pdf

School Choice: A Mechanism Design Approach

We investigate the "generalized second-price" (GSP) auction, a new mechanism used by search engines to sell online advertising. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. Unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP, we describe the generalized English auction that corresponds to GSP and show that it has a unique equilibrium. This is an ex post equilibrium, with the same payoffs to all players as the dominant strategy equilibrium of VCG.

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Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new "law of aggregate demand" for the case of discrete heterogeneous workers and show that, when workers are substitutes, this law is satisfied by profit-maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.,

/pdf/matching-with-contracts-3c5aa6cbwt.pdf

Matching with Contracts

http://pareto.uab.es/jmasso/pdf/HatfieldKojimaJET2010.pdf

Substitutes and stability for matching with contracts

We introduce a model in which agents in a network can trade via bilateral contracts. We find that when continuous transfers are allowed and utilities are quasi-linear, the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure. Furthermore, the set of stable outcomes is essentially equivalent to the set of competitive equilibria, and all stable outcomes are in the core and are efficient. By contrast, for any domain of preferences strictly larger than that of full substitutability, the existence of stable outcomes and competitive equilibria cannot be guaranteed.

/pdf/stability-and-competitive-equilibrium-in-trading-networks-4gvn9oelef.pdf

Stability and Competitive Equilibrium in Trading Networks

We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to-many) matching with contracts, as well as supply chain matching. When firms’ relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations are guaranteed to exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. ( C78, D85, D86, L14)

/pdf/matching-in-networks-with-bilateral-contracts-343lnryt00.pdf

Matching in Networks with Bilateral Contracts

The theory of two-sided matching markets has interested researchers for its theoretical appeal and its relevance to the design of real-world institutions. The medical residency matching mecha? nism in the United States, the National Resident Matching Program (NRMP), and student assign? ment systems in New York City and Boston are important mechanisms designed by economists using the theory.1 Hatfield and Paul R. Milgrom (2005) present a unified framework of matching with contracts, which includes the two-sided matching and package auction models as well as a simplified version of a labor market model of Alexander Kelso and Vincent P. Crawford (1982) as special cases. They introduce the substitutes condition of contracts, which is an adaptation of the substitutability condition in the matching literature (Roth and Marilda A. Oliveira Sotomayor 1990) to matching with contracts. They show that there exists a stable allocation if contracts are substitutes for hospitals, and that a number of other results in matching generalize to problems with contracts. They further claim that the substitutes condition on individual hospitals' prefer? ences is necessary to guarantee the existence of a stable allocation for all possible singleton preferences of others: that is, if contracts are not substitutes for a hospital, then there exists a preference profile of other hospitals with single job openings and doctors such that there exists no stable allocation. We show that this last claim of Hatfield and Milgrom (2005) does not hold in general. The counterexample we present involves a hospital which has two different kinds of positions, and the preferences of the hospital are a combination of preferences of these two positions. While the substitutes condition does not hold for that hospital, we adopt a technique developed by Bettina Klaus and Flip Klijn (2005) and show that there exists a stable allocation. We then present the weak substitutes condition, which we show is necessary to guarantee existence of stable allocations. The modified result we present, as well as the original contribu? tion of Hatfield and Milgrom (2005), suggest a connection between the substitutes condition and stability.2

/pdf/matching-with-contracts-comment-3aohybsv3f.pdf

John William Hatfield

Papers

Matching with Contracts

Substitutes and stability for matching with contracts

Stability and Competitive Equilibrium in Trading Networks

Matching in Networks with Bilateral Contracts

Matching with Contracts: Comment