We study how asymmetric information affects the set of rationalizable solutions in a linear setup where the outcome is determined by forecasts about this same outcome. The unique rational expectations equilibrium is also the unique rationalizable solution when the sensitivity of the outcome to agents' forecasts is less than one, provided that this sensitivity is common knowledge. Relaxing this common knowledge assumption, multiple rationalizable solutions arise when the proportion of agents who know the sensitivity is large, and the uninformed agents believe it is possible that the sensitivity is greater than one. Instability is equivalent to existence of some kind of sunspot equilibria.