  We study how privacy technologies affect user and advertiser behavior in a
simple economic model of targeted advertising. In our model, a consumer first
decides whether or not to buy a good, and then an advertiser chooses an
advertisement to show the consumer. The consumer's value for the good is
correlated with her type, which determines which ad the advertiser would prefer
to show to her---and hence, the advertiser would like to use information about
the consumer's purchase decision to target the ad that he shows.
  In our model, the advertiser is given only a differentially private signal
about the consumer's behavior---which can range from no signal at all to a
perfect signal, as we vary the differential privacy parameter. This allows us
to study equilibrium behavior as a function of the level of privacy provided to
the consumer. We show that this behavior can be highly counter-intuitive, and
that the effect of adding privacy in equilibrium can be completely different
from what we would expect if we ignored equilibrium incentives. Specifically,
we show that increasing the level of privacy can actually increase the amount
of information about the consumer's type contained in the signal the advertiser
receives, lead to decreased utility for the consumer, and increased profit for
the advertiser, and that generally these quantities can be non-monotonic and
even discontinuous in the privacy level of the signal.
