Inequalities and Wealth exchanges in a dynamical social network

1. 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

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

3. Pareto´s law

4. Pareto’s power law

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

6. Wage distribution in Brazil

7. GNI 2002

8. A Conservative SOC Model • Each agent is characterized by awealth-parameter(the “fitness” in the original model). Agents have closer ties with nearest neighbors. • Rule to update the wealth: to look for the lowest wealthsite, 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)

9. Conservative model Threshold  0.42

10. Comparing inequalities... Argentina 2004 Argentina 1974

11. ...with the simulations

12. 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 (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 • This transaction occurs with probability of favor the poorer agentp, 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

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

14. Minimum Dynamics Random, p Scafetta formula  static If f < 0.4 the distribution is uniform, for f > 0.4 it is an exponential f=0.4

15. 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

16. Dynamic network distributions f=0.15

17. f=0.50

18. Wealth distribution f=0.1 f=0.5

19. Risk distribution f=0.5 f=0.1

20. Links distribution f=0.5 f=0.1

21. Lorenz curves f=0.5 f=0.1

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

23. Correlation between risk aversion and wealth

24. Wealth depending interactions Agents only interact when their wealth is within a threshold u |wi-wk| < u

25. Correlations between Wealth and Risk-aversion

26. Gini coefficients

27. 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, soa 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.