Equations vs. Maps: Complexity, Equilibrium, Disequilibrium

Abstract:

A key theme of complexity economics is nonequilibrium/disequilibrium dynamics. However, it is often not clear what this precisely means, leading to confusion about the differences and relative advantages of, for instance, general equilibrium and nonequilibrium agent-based models. In this chapter, I first review and survey economists on what equilibrium means. Answers range from equilibrium being a problem-specific concept with no general meaning to general definitions of equilibrium that may not be consistent with one another. Given this lack of consensus, I provide a novel definition. This definition is a technical, practical one: Equilibrium is when model variables are obtained by solving equations; nonequilibrium is when variables are just obtained as a map of other variables. Equilibrium and nonequilibrium can coexist in the same model, and nonequilibrium dynamics may converge to equilibrium. The main value added of our definition is that it clarifies the relative advantages of both equilibrium and nonequilibrium models. On the one hand, solving equations allows economists to determine variables without specifying an explicit process, making equilibrium models more parsimonious. On the other hand, nonequilibrium models such as agent-based models can easily accommodate many complexity-related ideas that are more difficult to include in equilibrium models, such as heterogeneity, nonlinear dynamics, and complex network structure.