1,714 research outputs found
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Spatial competition and price formation
We look at price formation in a retail setting, that is, companies set
prices, and consumers either accept prices or go someplace else. In contrast to
most other models in this context, we use a two-dimensional spatial structure
for information transmission, that is, consumers can only learn from nearest
neighbors. Many aspects of this can be understood in terms of generalized
evolutionary dynamics. In consequence, we first look at spatial competition and
cluster formation without price. This leads to establishement size
distributions, which we compare to reality. After some theoretical
considerations, which at least heuristically explain our simulation results, we
finally return to price formation, where we demonstrate that our simple model
with nearly no organized planning or rationality on the part of any of the
agents indeed leads to an economically plausible price.Comment: Minor change
SOC in a population model with global control
We study a plant population model introduced recently by J. Wallinga [OIKOS
{\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic',
`directed percolation'), but instead of using an infection or recovery rate as
control parameter, the population size is controlled directly and globally by
removing excess plants. We show that the model is very closely related to
directed percolation (DP). Anomalous scaling laws appear in the limit of large
populations, small densities, and long times. These laws, associated critical
exponents, and even some non-universal parameters, can be related to those of
DP. As in invasion percolation and in other models where the r\^oles of control
and order parameters are interchanged, the critical value of the wetting
probability is obtained in the scaling limit as singular point in the
distribution of infection rates. We show that a mean field type approximation
leads to a model studied by Y.C. Zhang et al. [J. Stat. Phys. {\bf 58}, 849
(1990)]. Finally, we verify the claim of Wallinga that family extinction in a
marginally surviving population is governed by DP scaling laws, and speculate
on applications to human mitochondrial DNA.Comment: 19 pages, with 10 ps-figured include
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