Nasdaq's management wanted to know whether this outcome would be repeated in a much larger and more intricate simulation that represented even more closely the exchange's day-to-day activities. So BiosGroup scientists built a $1 million-plus version of the model. This second virtual Nasdaq included agents playing the roles of upwards of 50 market makers as well as dozens of day traders, portfolio managers at large financial institutions and conservative individual investors. This time, the market makers were much closer replicas of their real-world counterparts—programmers used a vast amount of historical data and weeks of observation to closely mimic trading patterns—and the agents were taught to trade in many stocks at once. In addition, they were embedded with rules allowing them to learn from their experiences in the simulated model; set their quotes and execute their trades based on the highest profit they could generate from a transaction; handle all types of market orders, including straight transactions, limit orders and negotiated orders; and make trades on either Nasdaq's electronic system or on ECNs. Agents modeled after investors were given a huge amount of information for making trading decisions, including unsubstantiated rumors and verified news. They were programmed to decide whether to buy or sell by comparing the value that the available information gave to a stock with the price of the equity on Nasdaq or any other electronic marketplace. After hundreds of thousands of simulated runs, BiosGroup analysts determined that 70 percent of the time the model accurately reflected the real-world performance of market makers overall, and that the model could serve as the basis for further perfecting the model.

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As for the impact of decimalization on this model, says MacDonald, "second iteration, same outcome. Decimalization was clearly a threat to the established markets and to the equilibrium of price discovery."

That was valuable information for Berkeley: "It was a look at the mechanism of the markets, an inside view of the system that we never saw or documented before." For one thing, it explained, to a degree, what was happening in the dot-com bubble: Investors trading on noise and momentum, even with the larger fractional bid-ask gaps, were overpowering the stock market's traditional price discovery. For another, it provided ammunition to derail decimalization.

Berkeley presented the data that the agent-based model generated to the SEC and to Congress, hoping to persuade the regulators and lawmakers that decimalization could hinder the performance of the markets and harm investors. He was rebuffed. SEC officials were convinced that smaller increments would be a boon for individual investors. "They didn't want to hear it," says Berkeley. "There was a political mood to move to pennies and even the facts couldn't stop it."