Yard Sale Wealth Model

This is a simple model of wealth dynamics inspired by the "Yard-Sale model" first proposed by [1] and expanded upon by [2].

This is a good introductory article explaining the model: https://www.scientificamerican.com/article/is-inequality-inevitable/

The model

All agents start with equal wealth. Agents are shown on a grid with each agent's wealth represented as the cell height on a logarithmic scale. The wealth dynamics are outlined as follows:

1. At each step an agent engages in at most one transaction with another agent.
2. In a transaction a fraction of the poorer agent's wealth is transferred. The direction of the transfer is determined by a coin flip.
3. The coin may be biased with a "wealth attained advantage".
4. At each time step wealth may be redistributed. Agents pay taxes and receive benefits. An agent with wealth greater than the average will see a reduction in their wealth, and vice-versa for an agent with wealth less than the average.

The plots window shows the wealth of the richest agent and the Gini coefficient over time.

Parameters

The simulation is controlled with the following global parameters:

1. wealth_transfer_rate: the proportion of the poorer agent's wealth transferred during each transaction. Can take values in the range [0, 1].
2. tax_rate: the proportion of each agent's wealth which is taxed and redistributed at each time step. Can take values in the range [0,1].
3. wealth_bias: the bias of the coin towards the agent with greater wealth in the transaction. A value of 0 implies no bias, i.e. a fair coin. Can take any non-negative value, but values in the range [0,5] should be sufficient to observe most behavior.

Wealth dynamics

Several interesting behaviors may be observed in the following cases.

Complete oligopoly

Without any redistribution, setting tax_rate = 0, eventually a single individual will hold all wealth. This is independent of the bias and the transfer rate.

Low inequality

Even a small tax rate is enough to prevent a single individual from controlling all the wealth. The simulation stays in an equilibrium, with wealth being redistributed among all agents at each time step.

Wealth attained advantage

Although taxes pull each agent's wealth towards the average wealth, biasing the transaction coin has the opposite effect, adding more variability into the wealth distribution. Even with some taxation, increasing wealth_bias will tend to condense wealth of the system in a small number of agents.

References

• [1] Distributions of money in model markets of economy, (https://arxiv.org/abs/cond-mat/0205221v1)

• [2] Oligarchy as a Phase Transition: The effect of wealth-attained advantage in a Fokker-Planck description of asset exchange (https://arxiv.org/abs/1511.00770v2)