Properties of wealth distribution in multi-agent systems of a complex network

We present a simple model for examining the wealth distribution with agents playing evolutionary games (the Prisoners’ Dilemma and the Snowdrift Game) on complex networks. Pareto’s power law distribution of wealth (from 1897) is reproduced on a scale-free network, and the Gibbs or log-normal distribution for a low income population is reproduced on a random graph. The Pareto exponents of a scale-free network are in agreement with empirical observations. The Gini coefficient of an ER random graph shows a sudden increment with game parameters. We suggest that the social network of a high income group is scale-free, whereas it is more like a random graph for a low income group.

[1]  Victor M. Yakovenko,et al.  Statistical mechanics of money , 2000 .

[2]  A. Colman.  Game Theory and its Applications: In the Social and Biological Sciences , 1995 .

[3]  F. C. Santos,et al.  Graph topology plays a determinant role in the evolution of cooperation , 2006, Proceedings of the Royal Society B: Biological Sciences.

[4]  Bikas K. Chakrabarti,et al.  Pareto Law in a Kinetic Model of Market with Random Saving Propensity , 2004 .

[5]  H. Takayasu,et al.  Zipf's law in income distribution of companies , 1999 .

[6]  R. Merton.  The Matthew Effect in Science , 1968, Science.

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[9]  M. BONITZ,et al.  Characteristics and impact of the matthew effect for countries , 1997, Scientometrics.

[10]  R. Mantegna,et al.  Zipf plots and the size distribution of firms , 1995 .

[11]  Michael Doebeli,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2004, Nature.

[12]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[13]  Victor M. Yakovenko,et al.  Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States , 2001, cond-mat/0103544.

[14]  Wenxu Wang,et al.  Memory-based snowdrift game on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[16]  Sitabhra Sinha.  Evidence for Power-law tail of the Wealth Distribution in India , 2006 .

[17]  Bikas K. Chakrabarti,et al.  Econophysics of Wealth Distributions , 2005 .

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  Rui Jiang,et al.  A unified framework for the pareto law and Matthew effect using scale-free networks , 2006, physics/0606085.

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

[21]  Yoshi Fujiwara,et al.  Growth and fluctuations of personal income , 2002 .

[22]  S. Solomon,et al.  NEW EVIDENCE FOR THE POWER-LAW DISTRIBUTION OF WEALTH , 1997 .

[23]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[24]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Bing-Hong Wang,et al.  Role of connectivity-induced weighted words in language games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Bikas K. Chakrabarti,et al.  Kinetic exchange models for income and wealth distributions , 2007, 0709.1543.

[27]  Bikas K. Chakrabarti,et al.  Statistical mechanics of money: how saving propensity affects its distribution , 2000, cond-mat/0004256.

[28]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[29]  Li Zhang,et al.  The Circulation of Money and Holding Time Distribution , 2003, physics/0507147.

[30]  D. F. Brewer.  The ‘Matthew’ Effect: The Gospel Truth , 1991 .

[31]  Wen-Xu Wang,et al.  Effects of average degree on cooperation in networked evolutionary game , 2006 .

[32]  R. Wade.  The Causes of Increasing World Poverty and Inequality; Or, Why the Matthew Effect Prevails , 2004, International journal of health services : planning, administration, evaluation.

[33]  Alasdair I. Houston,et al.  Variation in behaviour promotes cooperation in the Prisoner's Dilemma game , 2004, Nature.