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Follow the Money

Brian Hayes

Beyond the Dreams of Avarice

The recent publications on asset-exchange models describe many more variations. Dragulescu and Yakovenko mention a family of models that differ among themselves only in the rule for choosing an amount of money to transfer. In one case it is a small fixed quantity; in another it is a random fraction of the trading pair's average wealth; in a third model the amount is a random fraction of the average wealth of the entire population. To avoid putting traders into debt or bankruptcy, Dragulescu and Yakovenko apply the meta-rule that if the loser cannot pay, the entire transaction is canceled. In all these models the equilibrium distribution has an exponential form, and there is no economic collapse.

Figure 3. A subtle change in the economic model . . .Click to Enlarge Image

Ispolatov, Krapivsky and Redner look at greedy or exploitative rules, where the wealthier party always wins the exchange (perhaps reflecting a situation where the poor have less bargaining power). When the amount transferred is a random fraction of the poorer's agent's wealth (as in the yard-sale model), the result is economic collapse, with all funds gravitating toward one person. Of course it's hardly a surprise that systematic greed yields a harsh outcome. The surprise is that this obviously biased rule is no worse than the symmetrical rule in the yard-sale model.

Chakraborti looks at the effect of savings, allowing traders to hold back some of their capital from the market. In the yard-sale economy, savings cannot forestall a collapse. Reserving a fixed sum of money shifts the minimum wealth up from zero but does not alter the dynamics of the model. Saving a fixed fraction of wealth slows the collapse, but the winner still takes all in the end.

Several authors mention the effects of taxes, welfare and other explicit means of redistributing income. Imposing a tax on wealth prevents the implosion of the yard-sale economy (see Figure 4), but the effects of an income tax are not so clear. I experimented with income taxes by collecting a percentage of each transaction and redistributing the proceeds in equal shares to all traders. A low tax rate does not protect against collapse, but models with tax rates higher than about 15 percent do seem to survive indefinitely. If there is a sharp threshold between these regimes, I have been unable to identify it.

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