Distorted Voronoi languages

In a recent paper, Jäger, Metzger, and Riedel (2011) study communication games of common interest when signals are simple and types complex. They characterize strict Nash equilibria as so-called Voronoi languages that consist of Voronoi tesselations of the type set and Bayesian estimators on the side of receivers. In this note, we introduce conflicts of interest in the same setting. We characterize strict Nash equilibria as distorted Voronoi languages that use all messages. For large conflicts, such informative equilibria need not exist. If the bias is sufficiently small, however, these equilibria do exist. This establishes the robustness of the results in Jäger, Metzger, and Riedel (2011) to biased interests. We finally give examples of strict Nash equilibria, one of them using simulations to illustrate an equilibrium with many messages and non-uniformly distributed types.