On Bayesian Persuasion with Multiple Senders

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 play pure strategies. This paper shows that these three conditions are also necessary to the result. In sequential persuasion games, the order of moves matters, and we show that adding a sender as a first mover and keeping the order of moves fixed for the other senders cannot result in a loss of information.