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 $p_c$ of the wetting probability $p$ 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