Information Choice Technologies: Technical Appendix

Proof. Proof of claim 1: Suppose all agents acquire full information. In this case Π(bi) = 0 and each agent has to pay c. Deviating from the equilibrium means that the agent receives an uninformative signal, i.e. bi → ∞, but does not have to pay c. From the definition we can easily see that as bi → ∞, τv → 0. In the full information equilibrium, the agent knows that ā = s and thus Var [ā|Ii] = Cov [ā, s|Ii] = Var [s|Ii]. Put differently, the agent only needs to forecast s, as he knows the action of the other players. Thus, after deviation, the agent’s payoff becomes