2,083 research outputs found
Descending Price Optimally Coordinates Search
Investigating potential purchases is often a substantial investment under
uncertainty. Standard market designs, such as simultaneous or English auctions,
compound this with uncertainty about the price a bidder will have to pay in
order to win. As a result they tend to confuse the process of search both by
leading to wasteful information acquisition on goods that have already found a
good purchaser and by discouraging needed investigations of objects,
potentially eliminating all gains from trade. In contrast, we show that the
Dutch auction preserves all of its properties from a standard setting without
information costs because it guarantees, at the time of information
acquisition, a price at which the good can be purchased. Calibrations to
start-up acquisition and timber auctions suggest that in practice the social
losses through poor search coordination in standard formats are an order of
magnitude or two larger than the (negligible) inefficiencies arising from
ex-ante bidder asymmetries.Comment: JEL Classification: D44, D47, D82, D83. 117 pages, of which 74 are
appendi
The geometry of manifolds and the perception of space
This essay discusses the development of key geometric ideas in the 19th
century which led to the formulation of the concept of an abstract manifold
(which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl
in 1913. This notion of manifold and the geometric ideas which could be
formulated and utilized in such a setting (measuring a distance between points,
curvature and other geometric concepts) was an essential ingredient in
Einstein's gravitational theory of space-time from 1916 and has played
important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064
Variational formulation of Eisenhart's unified theory
Eisenhart's classical unified field theory is based on a non-Riemannian
affine connection related to the covariant derivative of the electromagnetic
field tensor. The sourceless field equations of this theory arise from
vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate
Eisenhart's theory from the metric-affine variational principle. In this
formulation, a Lagrange multiplier constraining the torsion becomes the source
for the Maxwell equations.Comment: 7 pages; published versio
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
It is shown how to resolve the apparent contradiction between the macroscopic
approach of phase space and the validity of the uncertainty relations. The main
notions of statistical mechanics are re-interpreted in a quantum-mechanical
way, the ergodic theorem and the H-theorem are formulated and proven (without
"assumptions of disorder"), followed by a discussion of the physical meaning of
the mathematical conditions characterizing their domain of validity.Comment: English translation by Roderich Tumulka of J. von Neumann: Beweis des
Ergodensatzes und des H-Theorems. 41 pages LaTeX, no figures; v2: typos
corrected. See also the accompanying commentary by S. Goldstein, J. L.
Lebowitz, R. Tumulka, N. Zanghi, arXiv:1003.212
Implication of Compensator Field and Local Scale Invariance in the Standard Model
We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments
hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The
necessary ingredients for describing chaotic inflation in the SM as
entertained by Bezrukov and Shaposhnikov [17] have been provided by our
original model [8]. We regret their omission in citing our original model [8
Multidimensional Heterogeneity and Platform Design
One of the most salient issues faced by platforms like newspapers and
credit card issuers is that users are heterogeneous in the value they
bring to other users or to the platform. We develop a model with
multi-dimensional heterogeneity where a monopoly platform chooses (price
or non-price) instruments. Users play two roles: 1) they are users of
the platform’s services with heterogeneous preferences over
instruments and platform characteristics; 2) they make heterogeneous
contributions that endogenously determine these characteristics. The
marginal (private or social) value of an instrument or characteristic
includes the classical direct impact on profit and on (relevant)
participants’ utilities, but also includes a novel sorting effect
of marginal users and consequent further impact on platform
characteristics. The sorting effect is quantified by the covariance,
within the set of marginal users, between user preferences and user
contributions towards characteristics. The private optimum departs from
efficiency by prescribing lower quantities and catering to the tastes of
marginal (rather than average) users. Under reasonable conditions,
optimal allocations may be implemented uniquely by allowing each
instrument to be contingent on all characteristics. We discuss
applications to newspapers, broadcast media, credit cards, and suggest
simple extensions to the case of imperfect competition in insurance
provision and college admissions
Monomial integrals on the classical groups
This paper presents a powerfull method to integrate general monomials on the
classical groups with respect to their invariant (Haar) measure. The method has
first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)],
and is here used to obtain similar integration formulas for the unitary and the
unitary symplectic group. The integration formulas turn out to be of similar
form. They are all recursive, where the recursion parameter is the number of
column (row) vectors from which the elements in the monomial are taken. This is
an important difference to other integration methods. The integration formulas
are easily implemented in a computer algebra environment, which allows to
obtain analytical expressions very efficiently. Those expressions contain the
matrix dimension as a free parameter.Comment: 16 page
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