On the fragility of sunspot equilibria under learning and evolutionary dynamics

In this article, we investigate the possibility of sunspot equilibria to emerge from a process of learning and adaptation on agents' beliefs. We consider both finite state Markov sunspots and sunspots in autoregressive form, and derive conditions for the existence of an heterogeneous equilibrium where only a fraction of agents condition their forecasts on the sunspot. We then show that when the fraction of agents conditioning their forecasts on a sunspot changes over time, under evolutionary dynamics, these restrictions need to evolve endogenously with population shares. We argue that such requirement questions the possibility of sunspot equilibria to emerge through a process of evolution and adaptation on agents' beliefs: in order for a sunspot equilibrium to emerge, all agents must simultaneously coordinate on the same sunspot variable at the same time.