  The dual crises of the sub-prime mortgage crisis and the global financial
crisis has prompted a call for explanations of non-equilibrium market dynamics.
Recently a promising approach has been the use of agent based models (ABMs) to
simulate aggregate market dynamics. A key aspect of these models is the
endogenous emergence of critical transitions between equilibria, i.e. market
collapses, caused by multiple equilibria and changing market parameters.
Several research themes have developed microeconomic based models that include
multiple equilibria: social decision theory (Brock and Durlauf), quantal
response models (McKelvey and Palfrey), and strategic complementarities
(Goldstein). A gap that needs to be filled in the literature is a unified
analysis of the relationship between these models and how aggregate criticality
emerges from the individual agent level. This article reviews the agent-based
foundations of markets starting with the individual agent perspective of
McFadden and the aggregate perspective of catastrophe theory emphasising
connections between the different approaches. It is shown that changes in the
uncertainty agents have in the value of their interactions with one another,
even if these changes are one-sided, plays a central role in systemic market
risks such as market instability and the twin crises effect. These interactions
can endogenously cause crises that are an emergent phenomena of markets.
