Rajiv Sethi has an informative post on such models which, as he rightly claims, provides "microfoundations for macroeconomics in a manner that is both more plausible and more authentic than is the case with highly aggregative representative agent models". He defines them as "computational models in which a large numbers of interacting agents (individuals, households, firms, and regulators, for example) are endowed with behavioral rules that map environmental cues onto actions". He also writes that they generate "complex dynamics even with simple behavioral rules because the interaction structure can give rise to emergent properties that could not possibly be deduced by examining the rules themselves".
In a recent essay in Nature, Doyne Farmer and Duncan Foley make a strong case for the use of agent-based models in economics on the grounds that the existing econometric and DSGE based models suffer from the fatal flaw that they are fitted to past data and do not account for outlier (tail risk) events. They write,
"An agent-based model is a computerized simulation of a number of decision-makers (agents) and institutions, which interact through prescribed rules. The agents can be as diverse as needed — from consumers to policy-makers and Wall Street professionals — and the institutional structure can include everything from banks to the government. Such models do not rely on the assumption that the economy will move towards a pre-determined equilibrium state, as other models do. Instead, at any given time, each agent acts according to its current situation, the state of the world around it and the rules governing its behaviour.
An individual consumer, for example, might decide whether to save or spend based on the rate of inflation, his or her current optimism about the future, and behavioural rules deduced from psychology experiments. The computer keeps track of the many agent interactions, to see what happens over time. Agent-based simulations can handle a far wider range of nonlinear behaviour than conventional equilibrium models. Policy-makers can thus simulate an artificial economy under different policy scenarios and quantitatively explore their consequences...
Agent-based models potentially present a way to model the financial economy as a complex system, as Keynes attempted to do, while taking human adaptation and learning into account, as Lucas advocated. Such models allow for the creation of a kind of virtual universe, in which many players can act in complex — and realistic — ways. In some other areas of science, such as epidemiology or traffic control, agent-based models already help policy-making."
As Rajiv Sethi writes, one of the major reasons why agent-based models have so far failed to take off relates to the difficulty of defining decision rules for agents under differing conditions, and in evaluating the effects of different factors. Further, creating agent-based models for the whole economy "requires close feedback between simulation, testing, data collection and the development of theory", which in turn demands "serious computing power and multi-disciplinary collaboration among economists, computer scientists, psychologists, biologists and physical scientists with experience in large-scale modelling".
A few popular agent-based models include John Conway's Game of Life, Thomas Schelling's segregation checkerboard, Leigh Tesfatsion's ACE.
Robert Axtell and Joshu Epstein have their silicon-based 'artificially intelligent agent-based social simulation' called the Sugarscape model. The Sugarscape includes the agents(inhabitants), the environment (two-dimensional grid) and the rules governing the interaction of the agents with each other and the environment. Eric Beinhocker provides an simple exploration of complexity economics and adaptively emergent systems in his book, The Origin of Wealth.
Update 1 (25/7/2010)
Economist has a nice summary of the research on ABMs. Unlike conventional models which use "representative agents (identical traders, firms or households whose individual behaviour mirrors the economy as a whole) and where interaction happens only indirectly through pricing, ABMs use a bottom-up approach which assigns particular behavioural rules to each agent (for example, some may believe that prices reflect fundamentals whereas others may rely on empirical observations of past price trends) and agents’ behaviour may be determined (and altered) by direct interactions between them. In an agent-based model you simply run a computer simulation to see what emerges, free from any top-down assumptions. It writes
"ABMs, in contrast, make no assumptions about the existence of efficient markets or general equilibrium. The markets that they generate are more like a turbulent river or the weather system, subject to constant storms and seizures of all sizes. Big fluctuations and even crashes are an inherent feature. That is because ABMs contain feedback mechanisms that can amplify small effects, such as the herding and panic that generate bubbles and crashes. In mathematical terms the models are “non-linear”, meaning that effects need not be proportional to their causes."