Reducible networks of economic agents with applications to trading strategies, financial stability and representative agents

If the nodes in a network have input-output responses satisfying a certain property (i.e. they are Prandtl-Ishlinskii (PI) operators) then remarkable simplifications are possible. For arbitrary network topologies (and under mild conditions) the aggregated response of the entire network can be rigorously reduced to that of a single aggregated agent. This is true even if cascading behaviour, such as bubbles and crashes, can occur in the network. We show how a common momentum trading strategy, known as a trailing stop, can be replicated using PI operators allowing for an analyzable agent-based momentum/herding market model. We then examine how such models can be used to try and quantify the stability of neoclassical/equilibrium solutions. Finally we show how boundedly rational inflation expectations can be rigorously aggregated to provide alternative representative agents for macroeconomic DSGE models.

Based on joint work with Pavel Krejčí, Eyram Kwame, Sergey Melnik, and Dmitrii Rachinskii.