46,091 research outputs found
Ordinal notions of submodularity
We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to Kreps [Kreps, D.M., 1979. A representation theorem for âPreference for Flexibilityâ. Econometrica 47 (3), 565â578] and one is a weakening of a notion due to Milgrom and Shannon [Milgrom, P., Shannon, C., 1994. Monotone comparative statics. Econometrica 62 (1), 157â180]. We show that any reflexive binary relation satisfying either of Krepsâs definitions also satisfies Milgrom and Shannonâs definition, and that any transitive and monotonic binary relation satisfying the Milgrom and Shannonâs condition satisfies both of Krepsâs conditions
Asymptotic Glosten Milgrom equilibrium
This paper studies the Glosten Milgrom model whose risky asset value admits
an arbitrary discrete distribution. Contrast to existing results on insider's
models, the insider's optimal strategy in this model, if exists, is not of
feedback type. Therefore a weak formulation of equilibrium is proposed. In this
weak formulation, the inconspicuous trade theorem still holds, but the
optimality for the insider's strategy is not enforced. However, the insider can
employ some feedback strategy whose associated expected profit is close to the
optimal value, when the order size is small. Moreover this discrepancy
converges to zero when the order size diminishes. The existence of such a weak
equilibrium is established, in which the insider's strategy converges to the
Kyle optimal strategy when the order size goes to zero
Milgrom's revision of cosmic dynamics: Amending Newton's laws or Keplers?
Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted
Dark matter and non-Newtonian gravity from General Relativity coupled to a fluid of strings
An exact solution of Einstein's field equations for a point mass surrounded
by a static, spherically symmetric fluid of strings is presented. The solution
is singular at the origin. Near the string cloud limit there is a
correction to Newton's force law. It is noted that at large distances and small
accelerations, this law coincides with the phenomenological force law invented
by Milgrom in order to explain the flat rotation curves of galaxies without
introducing dark matter. When interpreted in the context of a cosmological
model with a string fluid, the new solution naturally explains why the critical
acceleration of Milgrom is of the same order of magnitude as the Hubble
parameter.Comment: 12 pages, REVTeX, no figure
A new approach to the envelope theorem
We study the di€erentiability of the value function of a constrained optimization problem. We consider the envelope-theorem framework of Milgrom and Segal (2002), and we accomplish two goals. We show how one can relax Milgrom and Segalâs assumption that the choice set does not vary with parameters. More importantly, we develop a new approach to proving the di€erentiability of the value function. The key idea and main mathematical tool we employ in our approach are a novel feature in the literature dealing with the di€erentiability of the value function.value function, uniform convergence, di€erentiability, cor-
Exact results concerning multifield moduli of two-phase composites
Chen has recently shown how the response matrix of a two-phase composite can
be written as linear combinations of products of the component matrices. We
elaborate on Chen's expansions by deriving them in a different way, which a.
shows them in a different light, and b. permits us to generalize them further.
As an application of our results we find exact microstructure-independent
relations between the moduli of the two components and those of any composite.
The body of these relations is equivalent to the compatibility relations of
Milgrom and Shtrikman (1989), but they are cast in a rather different form,
which has certain advantages. As an example, we show how any modulus of an
arbitrary two-phase composite can be written in closed form as a linear
combination of any other of its moduli, with coefficients that depend only
on the component moduli, but not on the volume fractions, or the
microstructure.Comment: 6 page
Milgrom Relation Models for Spiral Galaxies from Two-Dimensional Velocity Maps
Using two-dimensional velocity maps and I-band photometry, we have created
mass models of 40 spiral galaxies using the Milgrom relation (the basis of
modified Newtonian dynamics, or MOND) to complement previous work. A Bayesian
technique is employed to compare several different dark matter halo models to
Milgrom and Newtonian models. Pseudo-isothermal dark matter halos provide the
best statistical fits to the data in a majority of cases, while the Milgrom
relation generally provides good fits as well. We also find that Milgrom models
give mass-to-light ratios that roughly correlate with galaxy color, as
predicted by stellar population models. A subsample of galaxies in the Hydra
cluster follow a tight relation between mass-to-light and color, but one that
is significantly different from relations found in previous studies. Ruling out
the Milgrom relation with rotational kinematics is difficult due to systematic
uncertainties in the observations as well as underlying model assumptions. We
discuss in detail two galaxies for which the Milgrom relation appears to fail
and find that relaxing the assumption of constant stellar mass-to-light ratio
can maintain Milgrom models' viability.Comment: accepted for publication in The Astronomical Journal; 17 page
Affliation in Multi-Unit Auctions
We extend Milgrom and Weberâs affiliated valuations model to the multi-unit case with constant marginal valuations where 2 bidders compete for k identical objects. We show that the discriminatory auction has a unique equilibrium, that corresponds to Milgrom and Weberâs firstprice equilibrium. This unique equilibrium therefore leads to lower expected prices than the equilibrium of the English auction where the units are bundled together. Hence we show that in a common value auction of a single object where the object can be divided into k parts, it is not possible to increase revenue by using a multi-unit discriminatory auction. We discuss a possible application to Treasury auctions.Affiliated Valuations, Multi-Unit Auctions, Treasury Auctions.
Point process bridges and weak convergence of insider trading models
We construct explicitly a bridge process whose distribution, in its own
filtration, is the same as the difference of two independent Poisson processes
with the same intensity and its time 1 value satisfies a specific constraint.
This construction allows us to show the existence of Glosten-Milgrom
equilibrium and its associated optimal trading strategy for the insider. In the
equilibrium the insider employs a mixed strategy to randomly submit two types
of orders: one type trades in the same direction as noise trades while the
other cancels some of the noise trades by submitting opposite orders when noise
trades arrive. The construction also allows us to prove that Glosten-Milgrom
equilibria converge weakly to Kyle-Back equilibrium, without the additional
assumptions imposed in \textit{K. Back and S. Baruch, Econometrica, 72 (2004),
pp. 433-465}, when the common intensity of the Poisson processes tends to
infinity
The MOND limit from space-time scale invariance
The MOND limit is shown to follow from a requirement of space-time scale
invariance of the equations of motion for nonrelativistic, purely gravitational
systems; i.e., invariance of the equations of motion under (t,r) goes to
(qt,qr), in the limit a0 goes to infinity. It is suggested that this should
replace the definition of the MOND limit based on the low-acceleration behavior
of a Newtonian-MOND interpolating function. In this way, the salient, deep-MOND
results--asymptotically flat rotation curves, the mass-rotational-speed
relation (baryonic Tully-Fisher relation), the Faber-Jackson relation,
etc.--follow from a symmetry principle. For example, asymptotic flatness of
rotation curves reflects the fact that radii change under scaling, while
velocities do not. I then comment on the interpretation of the deep-MOND limit
as one of "zero mass": Rest masses, whose presence obstructs scaling symmetry,
become negligible compared to the "phantom", dynamical masses--those that some
would attribute to dark matter. Unlike the former masses, the latter transform
in a way that is consistent with the symmetry. Finally, I discuss the putative
MOND-cosmology connection in light of another, previously known symmetry of the
deep-MOND limit. In particular, it is suggested that MOND is related to the
asymptotic de Sitter geometry of our universe. It is conjectured, for example,
that in an exact de Sitter cosmos, deep-MOND physics would exactly apply to
local systems. I also point out, in this connection, the possible relevance of
a de Sitter-conformal-field-theory (dS/CFT) duality.Comment: 17 pages; Changed to match version to be published in The
Astrophysical Journa
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