13,718 research outputs found
Bartering integer commodities with exogenous prices
The analysis of markets with indivisible goods and fixed exogenous prices has
played an important role in economic models, especially in relation to wage
rigidity and unemployment. This research report provides a mathematical and
computational details associated to the mathematical programming based
approaches proposed by Nasini et al. (accepted 2014) to study pure exchange
economies where discrete amounts of commodities are exchanged at fixed prices.
Barter processes, consisting in sequences of elementary reallocations of couple
of commodities among couples of agents, are formalized as local searches
converging to equilibrium allocations. A direct application of the analyzed
processes in the context of computational economics is provided, along with a
Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table
Part I. The Cosmological Vacuum from a Topological Perspective
This article examines how the physical presence of field energy and
particulate matter can be interpreted in terms of the topological properties of
space-time. The theory is developed in terms of vector and matrix equations of
exterior differential systems, which are not constrained by tensor
diffeomorphic equivalences. The first postulate defines the field properties (a
vector space continuum) of the Cosmological Vacuum in terms of matrices of
basis functions that map exact differentials into neighborhoods of exterior
differential 1-forms (potentials). The second postulate requires that the field
equations must satisfy the First Law of Thermodynamics dynamically created in
terms of the Lie differential with respect to a process direction field acting
on the exterior differential forms that encode the thermodynamic system. The
vector space of infinitesimals need not be global and its compliment is used to
define particle properties as topological defects embedded in the field vector
space. The potentials, as exterior differential 1-forms, are not (necessarily)
uniquely integrable: the fibers can be twisted, leading to possible Chiral
matrix arrays of certain 3-forms defined as Topological Torsion and Topological
Spin. A significant result demonstrates how the coefficients of Affine Torsion
are related to the concept of Field excitations (mass and charge); another
demonstrates how thermodynamic evolution can describe the emergence of
topological defects in the physical vacuum.Comment: 70 pages, 5 figure
Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
Continuing on recent computational and experimental work on jammed packings
of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider
jamming in packings of smooth strictly convex nonspherical hard particles. We
explain why the isocounting conjecture, which states that for large disordered
jammed packings the average contact number per particle is twice the number of
degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to
nonspherical particles. We develop first- and second-order conditions for
jamming, and demonstrate that packings of nonspherical particles can be jammed
even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm
using these conditions to computer-generated hypoconstrained ellipsoid and
ellipse packings and demonstrate that our algorithm does produce jammed
packings, even close to the sphere point. We also consider packings that are
nearly jammed and draw connections to packings of deformable (but stiff)
particles. Finally, we consider the jamming conditions for nearly spherical
particles and explain quantitatively the behavior we observe in the vicinity of
the sphere point.Comment: 33 pages, third revisio
Geometric origin of mechanical properties of granular materials
Some remarkable generic properties, related to isostaticity and potential
energy minimization, of equilibrium configurations of assemblies of rigid,
frictionless grains are studied. Isostaticity -the uniqueness of the forces,
once the list of contacts is known- is established in a quite general context,
and the important distinction between isostatic problems under given external
loads and isostatic (rigid) structures is presented. Complete rigidity is only
guaranteed, on stability grounds, in the case of spherical cohesionless grains.
Otherwise, the network of contacts might deform elastically in response to load
increments, even though grains are rigid. This sets an uuper bound on the
contact coordination number. The approximation of small displacements (ASD)
allows to draw analogies with other model systems studied in statistical
mechanics, such as minimum paths on a lattice. It also entails the uniqueness
of the equilibrium state (the list of contacts itself is geometrically
determined) for cohesionless grains, and thus the absence of plastic
dissipation. Plasticity and hysteresis are due to the lack of such uniqueness
and may stem, apart from intergranular friction, from small, but finite,
rearrangements, in which the system jumps between two distinct potential energy
minima, or from bounded tensile contact forces. The response to load increments
is discussed. On the basis of past numerical studies, we argue that, if the ASD
is valid, the macroscopic displacement field is the solution to an elliptic
boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and
minor errors correcte
Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly
In this note we investigate stochastic Nash equilibrium problems by means of
monotone variational inequalities in probabilistic Lebesgue spaces. We apply
our approach to a class of oligopolistic market equilibrium problems where the
data are known through their probability distributions.Comment: 19 pages, 2 table
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
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