Modelling complexity

Agents of creation
Oct 9th 2003 | OXFORD
From The Economist print edition

Artificial “agents” can model complex systems

THEY certainly cannot be faulted for a lack of ambition. The scientists and engineers who gathered this week in Oxford for the first International Workshop on Complex Agent-Based Dynamic Networks are seeking to explain much of the world's behaviour through the use of “agents”. In this context, an agent is a program that acts in a self-interested manner in its dealings with numerous other agents inside a computer. This arrangement can mimic almost any interactive system: a stockmarket; a habitat; even a business supply-chain. If the constituent parts can be understood, the reasoning goes, some insight into the whole will follow.

The systems that agents have been most successful in modelling so far are financial markets. This is partly because of the obvious interest that people have in understanding such markets, and partly because one of the challenges in setting up an agent-based model is defining clearly what individual agents want. In a financial market that definition is easy: money.

Vince Darley, of Eurobios UK, a consultancy based in London, told the workshop about his efforts to model one such market, the NASDAQ stockmarket based in New York. In 2001, NASDAQ underwent “decimalisation”. It stopped denominating shares in sixteenths of a dollar, and instead divided its dollars into cents. That meant prices could move in smaller increments, which was thought to be a good thing. But NASDAQ's bosses feared there might be unpleasant unintended consequences of the change, so they commissioned Dr Darley and his colleagues to predict what might happen.

The predictions were not perfect: Dr Darley's agents traded larger volumes of shares than real people did. But other forecasts were accurate. In particular, the market became less efficient. This was because so-called parasitic strategies, which try to manipulate the system, work better with small increments.

Sanmay Das, of the Massachusetts Institute of Technology, also uses agents to study financial markets. His studies, though, are designed to illuminate the behaviour of individual market-makers, rather than whole markets.

A market-maker is attempting to find the “true” value of a share—that is, a price that reflects all the commercially significant information relevant to that share. In the model, this value is assigned arbitrarily and is not “told” to the agents. Instead, they have to work it out. An earlier result had shown that, in a competitive environment, one way to allow agents to compute the true value would be to enforce a “zero-profit” condition on them. This is a restriction on the prices that a market-maker sets for buying and selling shares such that, over time, that market-maker just breaks even.

Actually computing this condition is hard. Instead, Mr Das worked out a way to make a close approximation to the prices that result from the condition. The market-maker can then make money by selling for just slightly more and buying just slightly cheaper than the formula dictates.

When Mr Das simulated a market using this approximation, the results closely matched the statistics of real-world markets. Actual market-makers often behave instinctively, and have difficulty explaining exactly why they set prices as they do. Mr Das's results make the reasons for this unconscious behaviour explicit.

The world as we don't know it

Financial markets are not the only game that agents can play. Neil Johnson, a physicist from Oxford University, told the workshop of his latest research on the so-called minority game. This is a stylised version of a classic problem: a big crowd enters a bar where there are fewer seats than people (or agents). Each individual decides independently whether to stay in the bar or leave. The process is then repeated indefinitely.

Recalling one of Yogi Berra's famous observations, “nobody goes there anymore, it's too crowded,” the agents in such a game adopt a number of different strategies for dealing with the situation. Dr Johnson has dubbed those adhering to Mr Berra's maxim as the “anti-crowd”. By studying what the agents actually do, he is able to build up a mathematical model of their interactions.

Not, you might think, that useful. But he is already working with a group at NASA, America's aeronautics and space agency, which uses like methods to deal with futuristic aeroplane wings. Rather than having just one aileron to control their pitch, these wings have hundreds of little ones. Each is, in effect, an agent. It must decide, based on what it perceives the other ailerons are doing, whether to stay up (ie, stay at the bar) or turn down (leave the bar). The mathematics of the two processes are surprisingly similar.

Less similar, though potentially more surprising, is Dr Johnson's research into crime. He is beginning to study how various organised criminal and paramilitary groups in Colombia interact with one another. Each group is treated as an agent, and they slug it out inside the computer in a game of drugs, money and politics. Whether anything useful will result remains to be seen.

Janet Efstathiou's studies, though, are already proving their worth. Dr Efstathiou, who works in Oxford's Department of Engineering Science, is investigating commercial supply chains in factories and warehouses. Other researchers working in this field discussed how they asked people involved in such supply chains—supermarket buyers, for example—what strategies were followed. They then attempted to create artificial agents that followed similar strategies. The problem with this, as Dr Efstathiou pointed out, is twofold. Not only are people often inaccurate in their beliefs about themselves, but—especially in the business world—they lie.

Instead, she set out to measure what was actually going on in factories and warehouses. She and her team of graduate students spent hours watching and recording which machines were running when. They also looked at where goods were being moved to and from. She then compared her findings about what was really happening with what people claimed was happening on paperwork such as invoices. By checking how often these agreed, she could approximate the mathematical “entropy” of the system—a measure of how disordered it was.

A complicated factory, with many different assembly lines, can still be ordered if everything is proceeding according to plan. Even a simple one, by contrast, would be disordered if managers had no idea of what was happening. Dr Efstathiou's efforts to create a complete agent-based model of all this are still under construction, but the clear-minded attempt to quantify baffling concepts, such as how messy a factory is, seems to be leading her in a direction that might help managers to improve their productivity.

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