Inequalities and Wealth exchanges in a dynamical social network

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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
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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
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Paretos law
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Paretos power law
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Wealth distribution in Japan (1998)
Log-normal power law
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Wage distribution in Brazil
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GNI 2002
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A Conservative SOC Model

• Each agent is characterized by a wealth-parameter
  (the fitness in the original model). Agents
  have closer ties with nearest neighbors.
• 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)

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Conservative model
Threshold ? 0.42
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Comparing inequalities...
Argentina 2004
Argentina 1974
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...with the simulations
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A model with risk-aversion

• A random (or not) fraction, ?, of the agents
  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 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

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Monte Carlo dynamics ? Random and p with Scafetta
formula

• Monte Carlo dynamics
• ? random quenched
• f0.5 power law

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Minimum Dynamics ? Random, p Scafetta formula
? static If f lt 0.4 the distribution is
uniform, for f gt 0.4 it is an exponential f0.4 ?
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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

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Dynamic network distributions
f0.15
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f0.50
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Wealth distribution
f0.1
f0.5
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Risk distribution
f0.5
f0.1
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Links distribution
f0.5
f0.1
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Lorenz curves
f0.5
f0.1
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Gini Indexes
Links f 5 20 80
0.0 0.816 0.921 0.955
0.1 0.793 0.878 0.910
0.5 0.443 0.466 0.473
Static Network
Links f 5 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 f 5 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)
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Correlation between risk aversion and wealth
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Wealth depending interactions
Agents only interact when their wealth is within
a threshold u wi-wk lt u
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Correlations between Wealth and Risk-aversion
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Gini coefficients
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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.