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Exploring the impact of multi-agent wealth exchange model on inequality reduction

Suchismita Banerjee

Abstract

Binary kinetic exchange models, where money is shuffled between two agents at a time, reproduce the Boltzmann Gibbs exponential wealth distribution but cannot address the multi party trades common in real markets. We generalize the exchange rule to simultaneous interactions among more than two agents in a closed economical system. We observe, as number of agents grow, the stationary wealth distribution evolves smoothly from an exponential to an almost uniform distribution. Inequality metrics (Gini and k index) has been found to fall monotonically with the increase in agents number. Compared with binary models that rely on saving propensities, which is also known to reduce inequality, we find the multi agent interaction show a completely different behavior of inequality reduction.

Exploring the impact of multi-agent wealth exchange model on inequality reduction

Abstract

Binary kinetic exchange models, where money is shuffled between two agents at a time, reproduce the Boltzmann Gibbs exponential wealth distribution but cannot address the multi party trades common in real markets. We generalize the exchange rule to simultaneous interactions among more than two agents in a closed economical system. We observe, as number of agents grow, the stationary wealth distribution evolves smoothly from an exponential to an almost uniform distribution. Inequality metrics (Gini and k index) has been found to fall monotonically with the increase in agents number. Compared with binary models that rely on saving propensities, which is also known to reduce inequality, we find the multi agent interaction show a completely different behavior of inequality reduction.
Paper Structure (15 sections, 10 equations, 6 figures, 2 tables)

This paper contains 15 sections, 10 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Models of multi-agent kinetic wealth exchange
  3. Binary benchmark $(n=2)$
  4. Triadic exchange $(n=3)$
  5. Tetradic exchange $(n=4)$
  6. Pentadic exchange $(n=5)$
  7. Hexadic exchange $(n=6)$
  8. Type I (two independent triplets)
  9. Type II (three independent binary splits)
  10. Summary of exchange kernels
  11. Simulation parameter choices and validation of the robustness
  12. Result and Discussion
  13. Emergent wealth distributions for multi-agent exchange:
  14. Inequality metrics: Lorenz, Gini and Kolkata indices for multi-agent exchange:
  15. Comparison of multi-agent exchange with binary saving-propensity models

Figures (6)

  • Figure 1: Robustness checks for the triadic kernel. Left: collapse of probability density functions for different total number of agents; Right: overlap of the same for different number of total iteration.
  • Figure 2: Wealth distribution for 6-agent interaction considering two different types of interaction kernels.
  • Figure 3: Distribution of wealth for 3 agent, 4 agent, 5 agent and 6 agent wealth exchange models and comparison with 2 agent exchange model.
  • Figure 4: Lorenz curves, Gini ($g$) and Kolkata ($k$) indices for different multi-agent interactions.
  • Figure 5: $g$ vs $k$-index for different multi-agent interactions.
  • ...and 1 more figures