  We study the canonical signaling game, endowing the sender with commitment
power: before learning the state, sender designs a strategy, which maps the
state into a probability distribution over actions. We provide a geometric
characterization of the sender's attainable payoffs, described by the
topological join of the graphs of the interim payoff functions associated with
different sender actions. We extend the sender's commitment power to the design
of a communication protocol, characterizing whether and how sender benefits
from revealing information about the state, beyond what is inferred from his
action. We apply our results to the design of adjudication procedures, rating
or grading systems, and sequencing algorithms for online platforms.
