Nasdaq's Brown was a recent and enthusiastic convert to complexity theory when Berkeley asked him for help in solving the dot-com quandary. Just a short time earlier, on his way to a conference, Brown began to read Kauffman's At Home in the Universe (Oxford University Press, 1995). He was so enthralled by the explanations of the way enterprises work and by the descriptions of how agents at the lowest systems level can determine the efficiency of upper-tier operations that he couldn't put the book down. In fact, he stayed in his hotel room throughout the next day reading it—and missed the conference entirely. Soon after, Brown called Kauffman and the pair held long discussions about the ways companies might use complexity theory to understand and improve their performance. When Berkeley asked for help, Brown was excited about the possibility of seeing BiosGroup's agent-based modeling approach first-hand at the exchange.

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During the initial meetings in 1998 between Nasdaq and BiosGroup, the decision was made to start with a simple model of the exchange to see if Nasdaq's real-world performance could be replicated. Nasdaq, an electronic exchange, essentially links market makers and other stock transaction companies over a network to manage the purchase and sale of about 3,600 stocks. Most market makers oversee dozens if not hundreds of different stocks, and their primary responsibility is to keep a stock liquid by matching buy and sell orders as they are placed, even if they have to use their own money to do so. While Nasdaq makes money from fees from listed companies, distributing market data and other financial products, it relies on market makers for much of its revenue, chiefly through a transaction charge placed on every trade executed on the exchange.

To construct the first Nasdaq model, BiosGroup scientists programmed eight different broker-dealer agents into the system, each of them acting as the market maker in a single stock. These agents, which were designed based on detailed records of trading patterns and interviews with market makers, were embedded with rules that allowed them to observe order flow through the simulation and to adapt their trading strategies as market conditions changed. If there was an influx of investors into a particular stock, for instance, the market maker could react by changing the quote. Investors were represented by about 50 different agents.

After running a series of simple mock trades that validated the prototype's ability to operate as an electronic market, the BiosGroup team proceeded to test the impact of decimalization on the model and on the way the model's agents interacted, in hopes of obtaining clues about how the real Nasdaq would react—a particularly timely experiment, because the SEC was then preparing to order U.S. exchanges to switch to share-price increments of a penny by mid-2000 (the deadline eventually was postponed until the following April). Nasdaq officials were concerned about this new equity tick, because its market makers generate their profits from the difference between the price at which a stock can be sold and the price at which it can be bought—the bid and the ask. Nasdaq management worried that if decimalization narrowed this gap by 51/4 cents, earnings of the market makers would suffer. In response, the dealers might try new trading strategies to avoid shortfalls. They might, for instance, avoid some small trades because the effort wasn't worth the meager profits these transactions would provide. Or they might migrate to Nasdaq's newest rivals, other electronic exchanges, such as Instinet and Island, that link buyers and sellers directly. Because of their peer-to-peer efficiency, these so-called ECNs (electronic communications networks) have tended to offer narrower bid-ask gaps than Nasdaq; consequently, Nasdaq's market makers had generally avoided trading on them. But by narrowing the spreads, decimalization could take away Nasdaq's competitive advantage—especially because some ECNs pay fees to market makers for shifting business to them. These and numerous other complex possibilities might reduce the number of transactions market makers execute on Nasdaq and thus trim its revenue.

When decimalization was introduced into the BiosGroup model, the average bid-ask spread, not surprisingly, narrowed: Often, the gap was only a penny. But the simulation's market-maker agents continued to trade with each other with no slowdown in activity. And so-called price discovery—which measures whether a stock is trading at its appropriate value (based on fundamental measures such as price-to-earnings ratios), and whether its price is responding appropriately to corporate events such as acquisitions, earnings reports and executive changes—was unaffected.

Then the modelers introduced aggressive day traders—investors programmed to take a chance on stocks if their analysis indicated that they could turn it quickly for a fast profit—into the simulation. As the post-decimalization bid-ask increment became smaller, gambles became less risky: Instead of a sixteenth of a dollar between the bid and ask, the gap was only a penny—and agents playing day traders saw their opening. The system was inundated with these speculative trades. The result: The share prices in the model no longer truly reflected company performance and business conditions. In other words, the agent-based model began to generate the very distant beginnings of a bubble. "It was a completely unexpected result: Letting rogue traders participate in the model to the extent that they would actively in the real world when the bid-ask decreases overwhelmed the market, and we lost both price discovery and liquidity," says Bob MacDonald, former CEO at BiosGroup and now a director at NuTech Solutions, which purchased BiosGroup earlier this year. "It wasn't an absolute characteristic of the market that you lost price discovery. It just occurred when investors were scrambling in between a small bid and ask gap."