Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Staphylococcus aureus virulence factors identified by using a high-throughput Caenorhabditis elegans-killing model

Staphylococcus aureus is an important human pathogen that is also able to kill the model nematode Caenorhabditis elegans. We constructed a 2,950-member Tn917 transposon insertion library in S. aureus strain NCTC 8325. Twenty-one of these insertions exhibited attenuated C. elegans killing, and of these, 12 contained insertions in different genes or chromosomal locations. Ten of these 12 insertions showed attenuated killing phenotypes when transduced into two different S. aureus strains, and 5 of the 10 mutants correspond to genes that have not been previously identified in signature-tagged mutagenesis studies. These latter five mutants were tested in a murine renal abscess model, and one mutant harboring an insertion in nagD exhibited attenuated virulence. Interestingly, Tn917 was shown to have a very strong bias for insertions near the terminus of DNA replication

Webteaching: sequencing of subject matter in relation to prior knowledge of pupils

Two experiments are discussed in which the sequencing procedure of webteaching is compared with a linear sequence for the presentation of text material.\ud \ud In the first experiment variations in the level of prior knowledge of pupils were studied for their influence on the sequencing mode of text presentation. Prior knowledge greatly reduced the effect of the size of sequencing procedures.\ud \ud In the second experiment pupils with a low level of prior knowledge studied a text, following either a websequence or a linear sequence. Webteaching was superior to linear teaching on a number of dependent variables. It is concluded that webteaching is an effective sequencing procedure in those cases where substantial new learning is required

Parameterized Supply Function Bidding: Equilibrium and Efficiency

We consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for a product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit maximizers. We consider a uniform price market design that uses supply function bidding: firms declare the amount they would supply at any positive price, and a single price is chosen to clear the market. We are interested in evaluating the impact of price-anticipating behavior both on the allocative efficiency of the market and on the prices seen at equilibrium. We show that by restricting the strategy space of the firms to parameterized supply functions, we can provide upper bounds on both the inflation of aggregate cost at the Nash equilibrium relative to the socially optimal level, as well as the markup of the Nash equilibrium price above the competitive level: as long as N > 2 firms are competing, these quantities are both upper bounded by 1 + 1/(N − 2). This result holds even in the presence of asymmetric cost structure across firms. We also discuss several extensions, generalizations, and related issues.National Science Foundation (U.S.) (Graduate Research Fellowship)National Science Foundation (U.S.) (grant ECS-0312921

A “laboratory of knowledge-making” for personal inquiry learning

We describe nQuire, a constraint-based learning toolkit to support a continuity of inquiry based learning between classroom and non-formal settings. The paper proposes design requirements for personal inquiry learning environments that support learning of personally meaningful science topics with development of metacognitive understanding and self-regulation of the scientific process through situated practice. It introduces a generic implementable model of the inquiry process, and describes an instantiation in the nQuire learning environment. An example of the use of the toolkit for a Healthy Eating inquiry with 28 Year 9 students concludes with results of the trial, design issues and recommendations

Biophysical Measurements of Cells, Microtubules, and DNA with an Atomic Force Microscope

Atomic force microscopes (AFMs) are ubiquitous in research laboratories and have recently been priced for use in teaching laboratories. Here we review several AFM platforms (Dimension 3000 by Digital Instruments, EasyScan2 by Nanosurf, ezAFM by Nanomagnetics, and TKAFM by Thorlabs) and describe various biophysical experiments that could be done in the teaching laboratory using these instruments. In particular, we focus on experiments that image biological materials and quantify biophysical parameters: 1) imaging cells to determine membrane tension, 2) imaging microtubules to determine their persistence length, 3) imaging the random walk of DNA molecules to determine their contour length, and 4) imaging stretched DNA molecules to measure the tensional force.Comment: 29 page preprint, 7 figures, 1 tabl

Strategy-Proofness and Efficiency with Nonquasi-Linear Preferences: A Characterization of Minimum Price Walrasian Rule

We consider the problems of allocating several heterogeneous objects owned by governments to a group of agents and how much agents should pay. Each agent receives at most one object and has nonquasi-linear preferences. Nonquasi-linear preferences describe environments in which large-scale payments influence agents' abilities to utilize objects or derive benefits from them. The minimum price Walrasian (MPW) rule is the rule that assigns a minimum price Walrasian equilibrium allocation to each preference profile. We establish that the MPW rule is the unique rule that satisfies the desirable properties of strategy-proofness, Pareto-efficiency, individual rationality, and nonnegative payment on the domain that includes nonquasi-linear preferences. This result does not only recommend the MPW rule based on those desirable properties, but also suggest that governments cannot improve upon the MPW rule once they consider them essential. Since the outcome of the MPW rule coincides with that of the simultaneous ascending (SA) auction, our result explains the pervasive use of the SA auction

Staphylococcal Biofilm Exopolysaccharide Protects against Caenorhabditis elegans Immune Defenses

Staphylococcus epidermidis and Staphylococcus aureus are leading causes of hospital-acquired infections that have become increasingly difficult to treat due to the prevalence of antibiotic resistance in these organisms. The ability of staphylococci to produce biofilm is an important virulence mechanism that allows bacteria both to adhere to living and artificial surfaces and to resist host immune factors and antibiotics. Here, we show that the icaADBC locus, which synthesizes the biofilm-associated polysaccharide intercellular adhesin (PIA) in staphylococci, is required for the formation of a lethal S. epidermidis infection in the intestine of the model nematode Caenorhabditis elegans. Susceptibility to S. epidermidis infection is influenced by mutation of the C. elegans PMK-1 p38 mitogen-activated protein (MAP) kinase or DAF-2 insulin-signaling pathways. Loss of PIA production abrogates nematocidal activity and leads to reduced bacterial accumulation in the C. elegans intestine, while overexpression of the icaADBC locus in S. aureus augments virulence towards nematodes. PIA-producing S. epidermidis has a significant survival advantage over ica-deficient S. epidermidis within the intestinal tract of wild-type C. elegans, but not in immunocompromised nematodes harboring a loss-of-function mutation in the p38 MAP kinase pathway gene sek-1. Moreover, sek-1 and pmk-1 mutants are equally sensitive to wild-type and icaADBC-deficient S. epidermidis. These results suggest that biofilm exopolysaccharide enhances virulence by playing an immunoprotective role during colonization of the C. elegans intestine. These studies demonstrate that C. elegans can serve as a simple animal model for studying host–pathogen interactions involving staphylococcal biofilm exopolysaccharide and suggest that the protective activity of biofilm matrix represents an ancient conserved function for resisting predation