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Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major…
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
In this Thesis we deal with problems regarding boundary behavior of analytic functions and approximation theory. We will begin by characterizing the set in which Blaschke products fail to have radial limits but have unrestricted limits on…
Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available…
Human cooperation depends on how accurately we infer others' motives--how much they value fairness, generosity, or self-interest from the choices they make. We model that process in binary dictator games, which isolate moral trade-offs…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
We establish the theorems that give necessary and sufficient conditions for an arbitrary function defined in the unit disk of complex plane in order to has boundary values along classes of equivalencies of simple curves. Our results…
Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals.…
Let $A$ be a von Neumann algebra with no direct summand of Type $\roman I_2$, and let $\scr P(A)$ be its lattice of projections. Let $X$ be a Banach space. Let $m\:\scr P(A)\to X$ be a bounded function such that $m(p+q)=m(p)+m(q)$ whenever…
The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the…
We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…
Classical optimal auction theory assumes that bids reach the seller directly. We study how this picture changes when a revenue-maximizing intermediary controls access to the seller's auction. Motivated by blockchain auctions, online…