On Bayesian persuasion with multiple senders

Hosted by Claudio Mezzeti

In a multi-sender Bayesian persuasion game, Gentzkow and Kamenica (2012) show that increasing the number of senders cannot decrease the amount of information revealed. They assume: (i) senders reveal information simultaneously, (ii) senders' information can be arbitrarily correlated, and (iii) senders cannot play mixed strategies. This paper shows that these conditions are not only sufficient but also necessary to obtain Gentzkow and Kamenica (2012)'s result. In sequential persuasion games, the order of moves matters, and we prove that adding a player as a first mover and keeping the order of moves fixed for the other players cannot result in a less informative equilibrium.