Inequalities and Wealth Inequalities and Wealth exchanges in a dynamical exchanges in a dynamical

social networksocial network

José Roberto IglesiasJosé Roberto IglesiasInstituto de Física, Faculdade de Ciências Instituto de Física, Faculdade de Ciências

Económicas, Económicas, U.F.R.G.S., Porto Alegre, BrazilU.F.R.G.S., Porto Alegre, Brazil

Kolkata, India, March 2005

J.R. Iglesias, S. PianegondaPorto Alegre, Brazil

S. GonçalvesPorto Alegre, Brazil

G. AbramsonS. C. de Bariloche, Argentina

J.L. VegaZurich, Switzerland

AuthorsAuthors

Fabiana LagunaS. C. de Bariloche, Argentina

•Sebastián Risau-Gusman•Vanessa H. de Quadros

Porto Alegre, Brazil

Pareto´s lawPareto´s law

Pareto’s power lawPareto’s power law

α)()(

ax

Ax

N

Wealth distribution in Japan (1998)Wealth distribution in Japan (1998)

Log-normal + power law

Wage distribution in BrazilWage distribution in Brazil

GNGNII 200 20022

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 A Conservative SOC ModelSOC Model

Conservative modelConservative model

Threshold 0.42

Comparing inequalities...Comparing inequalities...

Argentina 1974

Argentina 2004

...with the simulations...with the simulations

A model with risk-aversionA 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 (w1) exchanges with a random site (w2) a quantity:

The winner takes all, he gets all the quantity dw Variation of the model: The loser changes its value randomly

])1(;)1min[( 2211 wwdw

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/0209373v1

12

12

2

1

ww

wwfp

Monte Carlo dynamicsMonte Carlo dynamics Random and p with Scafetta formulaRandom and p with Scafetta formula

Monte Carlo dynamics random quenched f=0.5 power law12

12

2

1

ww

wwfp

Minimum Dynamics Minimum Dynamics Random, Random, pp Scafetta formula Scafetta formula

static

If f < 0.4 the distribution is uniform, for f > 0.4 it is an exponential

f=0.4

12

12

2

1

ww

wwfp

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 Dynamic network distributions

f=0.15

f=0.50

Wealth distributionWealth distribution

f=0.1 f=0.5

Risk distributionRisk distribution

f=0.1 f=0.5

Links distributionLinks distribution

f=0.1 f=0.5

Lorenz curvesLorenz curves

f=0.1 f=0.5

Gini IndexesGini IndexesLinks

f5 20 80

0.0 0.816 0.921 0.955

0.1 0.793 0.878 0.910

0.5 0.443 0.466 0.473Static Network

Links

f5 20 80

0.0 0.969 0.981 0.983

0.1 0.889 0.897 0.915

0.5 0.441 0.432 0.428

Only loser lost links (proportional to loses)

Links

f5 20 80

0.0 0.980 0.987 0.985

0.1 0.890 0.868 0.873

0.5 0.433 0.422 0.424

Winner win links from agents at random (proportional to gain)

Correlation between risk aversion and wealthCorrelation between risk aversion and wealth

Wealth depending interactionsWealth depending interactions

Agents only interact when their wealth is within a threshold u |wi-wk| < u

Correlations between Wealth and Risk-aversion

Gini coefficients

Concluding…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.