Topics in Information Economics | Collage of the Last Three Lectures
Costly Persuasion with Posterior-Separable Costs In the costly persuasion model, there is a cost $c(E)$ for experiment $E$. Assume it’s posterior separable: $$ c(E)=\mathbb E_{\mu\sim\langle E\mid\mu_0\rangle}[k(\mu)], $$ The sender chooses not only what information to reveal but also how much information to acquire. The entire problem collapses back into the familiar concavification framework: the sender’s interim value becomes $$ \hat v(\mu)=\mathbb E_\mu[v(a^*(\mu),\omega)]-k(\mu), $$ and optimal persuasion reduces to choosing a distribution of posteriors with mean $\mu_0$ to maximize its expectation. ...