  This review deals with several microscopic (``agent-based'') models of
financial markets which have been studied by economists and physicists over the
last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch,
Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of
simulation approaches in financial economics, we first give a summary of the
Donangelo-Sneppen model of monetary exchange and compare it with related models
in economics literature. Our selective review then outlines the main
ingredients of some influential early models of multi-agent dynamics in
financial markets (Kim-Markowitz, Levy-Levy-Solomon). As will be seen, these
contributions draw their inspiration from the complex appearance of investors'
interactions in real-life markets. Their main aim is to reproduce (and,
thereby, provide possible explanations) for the spectacular bubbles and crashes
seen in certain historical episodes, but they lack (like almost all the work
before 1998 or so) a perspective in terms of the universal statistical features
of financial time series.
