  A game is introduced to study the effect of privacy in strategic
communication between well-informed senders and a receiver. The receiver wants
to accurately estimate a random variable. The sender, however, wants to
communicate a message that balances a trade-off between providing an accurate
measurement and minimizing the amount of leaked private information, which is
assumed to be correlated with the to-be-estimated variable. The mutual
information between the transmitted message and the private information is used
as a measure of the amount of leaked information. An equilibrium is constructed
and its properties are investigated.
