2001/10/10 by Stefan Bornholdt, Friedrich Wagner · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #cond-mat.stat-mech #q-fin.GN #q-fin.ST
paper · pdf · doi:10.1016/s0378-4371(02)01218-9
published as Physica A 316 (2002) 453-468 · 9 pages RevTeX, 5 figures PostScript
arxiv created 2001/10/10 · arxiv updated 2009/11/30
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.