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Stability of money: Phase transitions in an Ising economy

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  • Stefan Bornholdt
  • Friedrich Wagner

Abstract

The stability of money value is an important requisite for a functioning economy, yet it critically depends on the actions of participants in the market themselves. Here we model the value of money as a dynamical variable that results from trading between agents. The basic trading scenario can be recast into an Ising type spin model and is studied on the hierarchical network structure of a Cayley tree. We solve this model analytically and observe a phase transition between a one state phase, always allowing for a stable money value, and a two state phase, where an unstable (inflationary) phase occurs. The onset of inflation is discontinuous and follows a first order phase transition. The stable phase provides a parameter region where money value is robust and can be stabilized without fine tuning.

Suggested Citation

  • Stefan Bornholdt & Friedrich Wagner, 2001. "Stability of money: Phase transitions in an Ising economy," Papers cond-mat/0110201, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0110201
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