Strong Duality for a Multiple-Good Monopolist

We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure $\mu$ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for $n$ independent uniform items each supported on $[c,c+1]$ is a grand-bundling mechanism, as long as $c$ is sufficiently large, extending Pavlov's result for $2$ items [Pavlov'11]. At the same time, our characterization also implies that, for all $c$ and for all sufficiently large $n$, the optimal mechanism for $n$ independent uniform items supported on $[c,c+1]$ is not a grand bundling mechanism

Mechanism Design via Optimal Transport

Optimal mechanisms have been provided in quite general multi-item settings [Cai et al. 2012b, as long as each bidder's type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting, e.g. when the bidders have additive valuations with independent and/or continuous values for the items, these results do not apply, and it was recently shown that exact revenue optimization is intractable, even when there is only one bidder [Daskalakis et al. 2013]. Even for item distributions with special structure, optimal mechanisms have been surprisingly rare [Manelli and Vincent 2006] and the problem is challenging even in the two-item case [Hart and Nisan 2012]. In this paper, we provide a framework for designing optimal mechanisms using optimal transport theory and duality theory. We instantiate our framework to obtain conditions under which only pricing the grand bundle is optimal in multi-item settings (complementing the work of [Manelli and Vincent 2006]), as well as to characterize optimal two-item mechanisms. We use our results to derive closed-form descriptions of the optimal mechanism in several two-item settings, exhibiting also a setting where a continuum of lotteries is necessary for revenue optimization but a closed-form representation of the mechanism can still be found efficiently using our framework.Alfred P. Sloan Foundation (Fellowship)Microsoft Research (Faculty Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship

The Complexity of Optimal Mechanism Design

Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders [18]. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless zpp ⊇ P[superscript #P]. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated. We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow-interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.Alfred P. Sloan Foundation (Fellowship)Microsoft Research (Faculty Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship

Low serum sphingolipids in children with attention deficit-hyperactivity disorder

Background: Attention deficit-hyperactivity disorder (ADHD) is the most prevalent neuropsychiatric condition in childhood. ADHD is a multifactorial trait with a strong genetic component. One neurodevelopmental hypothesis is that ADHD is associated with a lag in brain maturation. Sphingolipids are essential for brain development and neuronal functioning, but their role in ADHD pathogenesis is unexplored. We hypothesized that serum sphingolipid levels distinguish ADHD patients from unaffected subjects. Methods: We characterized serum sphingolipid profiles of ADHD patients and two control groups: non-affected relatives and non-affected subjects without a family history of ADHD. Sphingolipids were measured by LC-MS/MS in 77 participants (28 ADHD patients, 28 related controls and 21 unrelated controls). ADHD diagnosis was based on the Diagnostic and Statistical Manual of Mental Disorders (DSM IV-TR). Diagnostic criteria were assessed by 2 independent observers. Groups were compared by parametrical statistics. Results: Serum sphingomyelins C16:0, C18:0, C18:1, C24:1, ceramide C24:0 and deoxy-ceramide C24:1 were significantly decreased in ADHD patients at 20-30% relative reductions. In our sample, decreased serum sphingomyelin levels distinguished ADHD patients with 79% sensitivity and 78% specificity. Conclusions: Our results showed lower levels of all major serum sphingomyelins in ADHD. These findings may reflect brain maturation and affect neuro-functional pathways characteristic for ADHD

Community Colleges: School Community Relationships

The community college functions of community service and continuing education persistently tie the colleges\u27 goals and objectives to their surrounding communities. The community colleges have an opportunity to invest in their own future by embracing and nurturing their relationship with the community. This fostering of an enhanced school- community connection occurs when the colleges involve themselves in the educational, cultural, recreational, and social services of the community. The economic and business links to the community must be strengthened where they already exist and new programs promoted with an eye toward mutually beneficial endeavors

High levels of childhood obesity observed among 3- to 7-year-old New Zealand Pacific children is a public health concern.

This cross-sectional, community-based survey was designed to assess attained growth and body composition of 3- to 7-y-old Pacific children (n = 21 boys and 20 girls) living in Dunedin, New Zealand, and to examine nondietary factors associated with the percentage of body fat. Fat mass, lean tissue mass and the percentage of body fat were measured using dual energy X-ray absorptiometry. One trained anthropometrist also measured height, weight, skinfolds (triceps, subscapular) and circumferences (mid-upper arm, chest, waist, calf). Compared with the National Center for Health Statistics and National Health and Examination Surveys I and II reference data, these Pacific children were tall and heavy for their age with high arm-muscle-area-for-height. Median (quartiles) Z-scores for height and BMI-for-age and arm-muscle-area-for-height were 1.33 (0.60, 2.15), 1.20 (0.74, 4.43) and 1.09 (0.63, 1.85), respectively. Their median (quartile) percentage of body fat was 21.8% (15.0, 35.5) of which 38.5% was located in the trunk. The estimated percentage of children classified as obese ranged from 34 to 49% depending on the criterion used. Over 60% of the children had levels of trunk fat above 1 SD of reported age- and sex-specific Z-scores for New Zealand children. The nondietary factors examined (hours of television viewing and hours playing organized sports, as reported by parents) were not associated with variations in the percentage of body fat, after adjusting for age, sex and birth weight. These extremely high levels of obesity and truncal fat among very young New Zealand children will have major public health implications as these children age

A Quantitative Comparative Analysis of EdD Persistence Factors

Whether studying physical sciences, social sciences, engineering, mathematics, humanities, or education, approximately one in every two doctoral students fail to persist to degree completion (Bowen & Rudenstine, 1992; Lovitts, 2001; Tinto, 2012). A quantitative comparative study focused on two populations; students currently enrolled in the professional doctorate EdD program and former EdD students, including students who started but did not finish the program. Research-based variables, characterized as personal and program factors driving doctoral student attrition, were tested for significance. The participation criteria defined at least 80% of the program’s course content in totality was or is currently delivered online from a university offering the professional EdD degree, including affiliation with the Carnegie Project on the Education Doctorate (Allen & Seaman, 2015; Rockinson-Szapkiw et al., 2019). About half of the survey respondents attended an EdD program affiliated with the Carnegie Project on the Education Doctorate (CPED). In contrast, the other half attended an EdD program with no affiliation with CPED. The Community of Inquiry for Online Learning comprised four elements, teaching presence, social presence, cognitive presence, and emotional presence, and was the study’s theoretical framework. A total of [n = 725] individuals responded to surveys, which yielded a sample size of [n = 475] usable responses from former and current EdD students. The data from 30 former students, who did not persist, was analyzed for comparative purposes. Survey respondents represented a diverse population of age, gender, ethnicity, and marital status, attending public, private, and for-profit colleges and universities from geographic locations throughout the United States. The independent variable for all but the last of 16 hypothesis tests were current and former EdD students. The dependent variables were the personal and program factors. Five hypothesis tests included the effect of a moderating or second independent variable to reveal differences between the primary independent and dependent variables. The last hypothesis test compared time-to-degree between former students who attended an EdD program affiliated with the CPED and students who attended an EdD program with no affiliation with CPED. Within the 16 statements of hypothesis were 32 sub-hypotheses tests, of which the results indicated 19 were significant