Information transmission in nested sender–receiver games

We introduce a “nestedness” relation for a general class of sender–receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game B is nested in game A if the players’ optimal actions are closer in game B . We show that under some conditions, more information is transmitted in the nested game in the sense that the receiver’s expected equilibrium payoff is higher. The results generalize the comparative statics and welfare comparisons with respect to preferences in the seminal paper of Crawford and Sobel (Econometrica 50(6):1431–1452, 1982 ). We also derive new results with respect to changes in priors in addition to changes in preferences. We illustrate the usefulness of the results in three applications: (i) delegation to an intermediary with a different prior, (ii) the choice between centralization and delegation, and (iii) two-way communication with an informed principal.