Inequalities and Wealth exchanges in a dynamical social network José Roberto Iglesias Instituto de Física, Faculdade de Ciências Económicas, U.F.R.G.S., Porto Alegre, Brazil Kolkata, India, March 2005

J.R. Iglesias, S. Pianegonda Porto Alegre, Brazil S. Gonçalves Porto Alegre, Brazil G. Abramson S. C. de Bariloche, Argentina J.L. Vega Zurich, Switzerland Authors Fabiana Laguna S. C. de Bariloche, Argentina Sebastián Risau- Gusman Vanessa H. de Quadros Porto Alegre, Brazil

Pareto´s law

Pareto’s power law

Wealth distribution in Japan (1998) Log-normal + power law

Wage distribution in Brazil

GNI 2002

1.Each agent is characterized by a wealth-parameter ( the “fitness” in the original model ). Agents have closer ties with nearest neighbors. 2.Rule to update the wealth: to look for the lowest wealth site, to select in a random way its new wealth, and to deduce (or add) the wealth difference from (to) 2k - nearest neighbors (NN-version) or to random neighbors (R-version). ( In the original BS model the fitness of the neighbors is also choose at random). 3. Global wealth is constant (conservative model). 4. Agents may be in red (negative wealth) A Conservative SOC Model

Conservative model Threshold  0.42

Comparing inequalities... Argentina 1974 Argentina 2004

...with the simulations

A model with risk-aversion  A random (or not) fraction, , of the agent´s wealth is saved (A. Chatterjee et. al.)  The site with the minimum wealth (w 1 ) exchanges with a random site (w 2 ) a quantity:  The winner takes all, he gets all the quantity dw  Variation of the model: The loser changes its  value randomly  This transaction occurs with probability of favor the poorer agent p, being either p fixed for all the agents or p given by:  being f : 0  f  0.5 Ref: N. Scafetta, S. Picozzi and B. West, cond-mat/ v1

Monte Carlo dynamics  Random and p with Scafetta formula  Monte Carlo dynamics   random quenched  f=0.5 power law

Minimum Dynamics  Random, p Scafetta formula  static If f 0.4 it is an exponential f=0.4 

Dynamic Network Agents are distributed on a random lattice The average connectivity of the lattice is The winner receives “en plus” new links, either from the loser either from at site chosen at random Rich agents become more connected than poor ones

Dynamic network distributions f=0.15

f=0.50

Wealth distribution f=0.1f=0.5

Risk distribution f=0.1 f=0.5

Links distribution f=0.1 f=0.5

Lorenz curves f=0.1 f=0.5

Gini Indexes Links f Static Network Links f Only loser lost links (proportional to loses) Links f Winner win links from agents at random (proportional to gain)

Correlation between risk aversion and wealth

Wealth depending interactions Agents only interact when their wealth is within a threshold u |w i -w k | < u

Correlations between Wealth and Risk-aversion

Gini coefficients

Concluding… Gibbs (exponential) distribution of wealth appears in conservative without risk-aversion, independent on the number of neighbors and on the type of complex lattice. Minima dynamics generates states with a threshold or Poverty Line that do not appear in Monte Carlo simulations, so a fairer (less unequal) society because protects the weakest agents. Globalization increases the number of rich agents and the misery of the poorest ones. Risk-aversion introduces log-normal, exponential and power laws distributions. Correlation between wealth and connectivity, or Dynamic rewiring seems to induce a more realistic power law + exponential distribution.