A two-person game of information transmission

We consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities. One player is specialized in gathering information and transmitting it to the other, who takes the decision. This process is modeled as a game. Qualitative properties of the equilibria are analyzed. The impact of improving the quality of available information on the equilibrium welfares of the two individuals is studied. Better information generally may not improve welfare. We give conditions under which it will.