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A game is introduced to study the effect of privacy in strategic communication between a well-informed sender 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.

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Privacy-Constrained Communication**The work of F. Farokhi was supported by a McKenzie Fellowship, ARC grant LP130100605, a grant from Melbourne School of Engineering. The work of G. Nair was supported by ARC grants DP140100819 and FT140100527.