The Nash Equilibrium Revisited: Chaos and Complexity Hidden in Simplicity

Abstract: The Nash Equilibrium is a much discussed, deceptively complex, method for the analysis of non-cooperative games. If one reads many of the commonly available definitions the description of the Nash Equilibrium is deceptively simple in appearance. Modern research has discovered a number of new and important complex properties of the Nash Equilibrium, some of which remain as contemporary conundrums of extraordinary difficulty and complexity. Among the recently discovered features which the Nash Equilibrium exhibits under various conditions are heteroclinic Hamiltonian dynamics, a very complex asymptotic structure in the context of two-player bi-matrix games and a number of computationally complex or computationally intractable features in other settings. This paper reviews those findings and then suggests how they may inform various market prediction strategies.