Informational smallness in rational expectations equilibria

In an economy with asymmetric information, rational expectations equilibria (REE) need not become asymptotically incentive compatible, even if many independent replicas of the economy are merged together. We identify a sub-class of REE for which this is nevertheless the case. It consists of those REE which are focused-where close prices obtain in close state-wise posterior economies; and where the prices are rounded to whole "cents", so that very close exact prices cannot be distinguished. In this class of REE, the informational power of each agent does diminish as more and more similar agents join the market. In the limit economy with a continuum of replicas, the informational power of each individual is nullified completely in focused REE.