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Money and Goldstone modes

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  • P. Bak
  • S. F. Nrrelykke
  • M. Shubik

Abstract

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.

Suggested Citation

  • P. Bak & S. F. Nrrelykke & M. Shubik, 2001. "Money and Goldstone modes," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 186-190.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:186-190
    DOI: 10.1080/713665545
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    Cited by:

    1. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    2. Johann Lussange & Stefano Vrizzi & Stefano Palminteri & Boris Gutkin, 2024. "Modelling crypto markets by multi-agent reinforcement learning," Papers 2402.10803, arXiv.org.
    3. Martin Shubik & Eric Smith, 2005. "Fiat Money and the Natural Scale of Government," Cowles Foundation Discussion Papers 1509, Cowles Foundation for Research in Economics, Yale University.
    4. Smith, Eric & Shubik, Martin, 2011. "Endogenizing the provision of money: Costs of commodity and fiat monies in relation to the value of trade," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 508-530.

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