Second-order Price Dynamics: Approach to Equilibrium with Perpetual Arbitrage

TL;DR

This paper models second-order price dynamics showing that economies can persistently deviate from equilibrium with ongoing arbitrage opportunities, especially when heterogeneous actors and heuristics influence market behavior.

Contribution

It introduces a second-order dynamic framework explaining persistent deviations from equilibrium due to heterogeneous agents and arbitrage opportunities.

Findings

Economies can remain away from equilibrium with ongoing arbitrage.

Second-order dynamics naturally arise from heterogeneous agent behaviors.

Arbitrageurs exploit suboptimal heuristics repeatedly.

Abstract

The notion that economies should normally be in equilibrium is by now well-established; equally well-established is that economies are almost never precisely in equilibrium. Using a very general formulation, we show that under dynamics that are second-order in time a price system can remain away from equilibrium with permanent and repeating opportunities for arbitrage, even when a damping term drives the system towards equilibrium. We also argue that second-order dynamic equations emerge naturally when there are heterogeneous economic actors, some behaving as active and knowledgeable arbitrageurs, and others using heuristics. The essential mechanism is that active arbitrageurs are able to repeatedly benefit from the suboptimal heuristics that govern most economic behavior.