  In this dissertation two simple models of stock exchange are developed and
simulated numerically. The first is characterized by centralized trading with a
market maker. Unfortunately, this model is unable to generate realistic market
dynamics. The second model discards the requirement of centralized trading.
Under variation of the control parameter the model exhibits two phase
transitions: both a first- and a second-order (critical). The decentralized
model is able to capture many of the interesting properties observed in
empirical markets. Significantly, these properties only emerge when the
parameters are tuned such that the model spans the critical point. This
suggests that real markets may operate at or near a critical point, but is
unable to explain why this should be. One of the main points of the thesis is
that these empirical phenomena are not present in the stochastic driving force,
but emerge endogenously from interactions between agents.
