Statistical Economics on Multi-Variable Layered Networks

We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their peers' expectations (optimism/pessimism are contagious), while people living in the same neighborhood may influence their peers' saving patterns (stinginess/largeness are contagious). Thus, for each type of variable there exists a different underlying social network, which we refer to as a ``layer''. Each layer connects the same set of agents by a different set of links defining a different topology. In different layers, the nature of the variables and their dynamics may be different (Ising, Heisenberg, matrix models, etc). The different variables belonging to the same agent interact (the level of optimism of an agent may influence its saving level), thus coupling the various layers. We present a simple instance of such a network, where a one-dimensional Ising chain (representing the interaction between the optimist-pessimist expectations) is coupled through a random site-to-site mapping to a one-dimensional generalized Blume-Capel chain (representing the dynamics of the agents' saving ratios). In the absence of coupling between the layers, the one-dimensional systems describing respectively the expectations and the saving ratios do not feature any ordered phase (herding). Yet, such a herding phase emerges in the coupled system, highlighting the non-trivial nature of the present framework.

[1]  H. Capel.  On the possibility of first-order transitions in Ising systems of triplet ions with zero-field splitting III , 1967 .

[2]  D. Stauffer.  Introduction to statistical physics outside physics , 2003, cond-mat/0310037.

[3]  M. Blume.  THEORY OF THE FIRST-ORDER MAGNETIC PHASE CHANGE IN UO$sub 2$ , 1966 .

[4]  Robin R. Vallacher,et al.  Dynamical Social Psychology , 1998 .

[5]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[6]  Bruce W. Suter,et al.  The multilayer perceptron as an approximation to a Bayes optimal discriminant function , 1990, IEEE Trans. Neural Networks.

[7]  L. Festinger.  A Theory of Social Comparison Processes , 1954 .

[8]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[9]  Stefan Bornholdt,et al.  Stability of money: phase transitions in an Ising economy , 2001 .

[10]  Sorin Solomon,et al.  Theoretical analysis and simulations of the generalized Lotka-Volterra model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  S. Solomon,et al.  The importance of being discrete: life always wins on the surface. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Kurt Binder,et al.  A Guide to Monte Carlo Simulations in Statistical Physics , 2000 .

[13]  Steven N. Durlauf,et al.  Identification of binary choice models with social interactions , 2007 .

[14]  Population Censuses Surveys Office,et al.  Family Expenditure Survey Handbook , 1980 .

[15]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[16]  K. Malarz.  SOCIAL PHASE TRANSITION IN SOLOMON NETWORK , 2002, cond-mat/0210641.

[17]  P. Davidson.  Response [Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective] , 1991 .

[18]  S. Bikhchandani,et al.  Herd Behavior in Financial Markets; A Review , 2000 .

[19]  B. Latané,et al.  Statistical mechanics of social impact. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[20]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[21]  Socioeconomic interaction and swings in business confidence indicators , 2003, cond-mat/0312511.