Regensburg 2002 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 20: Mikro-ökonomische Modelle und Multi-Agenten-Systeme

AKSOE 20.3: Talk

Thursday, March 14, 2002, 17:00–17:30, H8

The stability of money in an Ising model economy — •Friedrich Wagner and Stefan Bornholdt — Institut für Theoretische Physik, Universität Kiel, Leibnizstr. 15, D-24098 Kiel

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. An early model by Bak and collaborators takes this into account and treats the value of money as a dynamical variable [1]. While they consider a one-dimensional chain of traders, where every agent always sells to the same neighbor, we extend this idea to a model on a higher dimensional network structure, introducing for each agent the option of choosing trading relationships [2]. This has dramatic consequences for the dynamics of the model. We recast the basic trading scenario into an Ising type spin model and study it 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.

[1] P. Bak, S.F. Norrelykke, and M. Shubik, Phys. Rev. E 60 (1999) 2528

[2] S. Bornholdt and F. Wagner, Stability of money: Phase transitions in an Ising economy, cond-mat/0110201 .