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Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth


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  • Sitabhra Sinha


We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a random fraction of the loser's wealth) asset exchange models. Several special cases including 2-player and 3-player versions of these `games' allow us to connect the results with observed features in real economies, e.g., lock-in (positive feedback), etc. We then implement the realistic notion that a richer agent is less likely to be aggressive when bargaining over a small amount with a poorer player. When this simple feature is added to the yard-sale model, in addition to the accumulation of the total wealth by a single agent ("condensation"), we can see exponential and power-law distributions of wealth. Simulation results suggest that the power-law distribution occurs at the cross-over of the system from exponential phase to the condensate phase.

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Paper provided by in its series Papers with number cond-mat/0304324.

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Date of creation: Apr 2003
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Publication status: Published in Physica Scripta, Vol. T 106, pp. 59-64 (2003)
Handle: RePEc:arx:papers:cond-mat/0304324

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Cited by:
  1. Sitabhra Sinha, 2005. "The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models," Papers physics/0504197,
  2. Venkat Venkatasubramanian, 2010. "What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions," Papers 1002.2269,
  3. Chakrabarti, Anindya S., 2011. "An almost linear stochastic map related to the particle system models of social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4370-4378.
  4. Arnab Chatterjee & Bikas K Chakrabarti, 2005. "Ideal-Gas Like Markets: Effect of Savings," Papers physics/0507136,, revised Jul 2005.
  5. J. R. Iglesias & R. M. C. de Almeida, 2011. "Entropy and equilibrium state of free market models," Papers 1108.5725,


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