Statistical mechanics of socio-economic systems with heterogeneous agents

Abstract

Abstract.We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and traffic modeling. We then focus on the analysis of the optimal properties of large random resource-allocation problems and on Minority Games and related models of speculative trading in financial markets, discussing a number of extensions including multi-asset models, Majority Games and models with asymmetric information. Finally, we summarize the main conclusions and outline the major open problems and limitations of the approach.

On Non-Ergodic Phases in Minority Games

“…as certain correlations between agents or, equivalently, transient parts of the dynamics are neglected. 6 Spherical models typically exhibit two types of ergodic phases, a frozen and an oscillatory one [9,25]. This appears to be the case for small λ > 0 as well, where as for large enough λ only the oscillatory phase appears to be present.…”

“…(16) for the re-scaled variable y i (t) = Γq i (t). The procedure is detailed in [6,21]. The resulting Langevin equation contains a noise term which accounts for the volatile decision dynamics:…”

“…This ensures that he estimates the profitability of strategy s using always the correct price return, namely that which would have occurred had he actually used s (see however [6] for a more thorough discussion). In order to allow for different degrees of agents' sophistication in the learning process, the following adjusted dynamics has been proposed [13]:…”

“…For this reason, it has drawn much interest from statistical physicists. Several monographs and reviews (as well as web resources) deal with the details of the model and we refer the reader to them for a more thorough introduction and motivation [3][4][5][6][7].…”

Diversity of scales makes an advantage: The case of the Minority Game

“…It is surely an exaggeration, as the complexity of the Ising model is many orders of magnitude higher, but nevertheless, the MG is a widely accepted framework for testing a variety of ideas in modelling socio-economic phenomena. There are several excellent reviews [8,9,10,11] of the vast literature on the subject, which we have no intention to review again here. The aim of our work is to contribute to understanding the possible advantages of diversity, which may be one of the sources of the heterogeneity of agents.…”