  The commitment power of senders distinguishes Bayesian persuasion problems
from other games with (strategic) communication. Persuasion games with multiple
senders have largely studied simultaneous commitment and signalling settings.
However, many real-world instances with multiple senders have sequential
signalling. In such contexts, commitments can also be made sequentially, and
then the order of commitment by the senders -- the sender signalling last
committing first or last -- could significantly impact the equilibrium payoffs
and strategies. For a two-sender persuasion game where the senders are
partially aware of the state of the world, we find necessary and sufficient
conditions to determine when different commitment orders yield different payoff
profiles. In particular, for the two-sender setting, we show that different
payoff profiles arise if two properties hold: 1) the two senders are willing to
collaborate in persuading the receiver in some state(s); and 2) the sender
signalling second can carry out a credible threat when committing first such
that the other sender's room to design signals gets constrained.
