Rich language and refinements of cheap-talk equilibria

I formalize the notion of equilibrium language, define the relation of having a richer language, and show the existence of equilibria with maximally rich language. I also study the stability of equilibria with respect to inflows of messages that can enrich their language, and provide examples of implausible cheap-talk equilibria, not refined away by the existing refinements, which can be refined away on the grounds of stability properties. ∗I am grateful to the two referees for their careful reading of the manuscript, and their many helpful remarks and suggestions. I would also like to thank for comments: Colin Campbell, Jeff Ely, Joel Sobel, the seminar participants at Northwestern University, the University of North Carolina at Chapel Hill and Duke University, the participants of the Society for Economic Design Conference in 2002. †Department of Economics, Nothwestern University, Evanston IL 60202