  We address Bayesian persuasion between a sender and a receiver with
state-dependent quadratic cost measures for general classes of distributions.
The receiver seeks to make mean-square-error estimate of a state based on a
signal sent by the sender while the sender signals strategically in order to
control the receiver's estimate in a certain way. Such a scheme could model,
e.g., deception and privacy, problems in multi-agent systems. Existing solution
concepts are not viable since here the receiver has continuous action space. We
show that for finite state spaces, optimal signaling strategies can be computed
through an equivalent linear optimization problem over the cone of completely
positive matrices. We then establish its strong duality to a copositive
program. To exemplify the effectiveness of this equivalence result, we adopt
sequential polyhedral approximation of completely-positive cones and analyze
its performance numerically. We also quantify the approximation error for a
quantized version of a continuous distribution and show that a semi-definite
program relaxation of the equivalent problem could be a benchmark lower bound
for the sender's cost for large state spaces.
