Heterogeneous sunspots solutions under learning and replicator dynamics

In a linear stochastic forward-looking univariate model with predetermined variables, we consider the possibility of heterogeneous equilibria with sunspots emerging endogenously through adaptive learning and replicator dynamics. In particular, we investigate equilibria where only a fraction of agents in the economy condition their forecasts on a sunspot, and equilibria where di¤erent groups of agents use di¤erent sunspots. We comclude that, although such heterogeneous equilibria exist and can be stable under adaptive learning, they do no survive under endogenous replicator dynamics. Moreover, we show that even homogeneous sunspot equilibria require some degree of coordinations among agents for them to emerge in an economy. We conclude that heterogeneous equilibria with sunspots are fragile under endogenous selection of predictors by agents, and that even the relevance of homogeneous sunspot equilibria is questioned once agents are allowed to doubt about the importance of sunspots in their forecasts.