  Businesses (retailers) often wish to offer personalized advertisements
(coupons) to individuals (consumers), but run the risk of strong reactions from
consumers who want a customized shopping experience but feel their privacy has
been violated. Existing models for privacy such as differential privacy or
information theory try to quantify privacy risk but do not capture the
subjective experience and heterogeneous expression of privacy-sensitivity. We
propose a Markov decision process (MDP) model to capture (i) different consumer
privacy sensitivities via a time-varying state; (ii) different coupon types
(action set) for the retailer; and (iii) the action-and-state-dependent cost
for perceived privacy violations. For the simple case with two states ("Normal"
and "Alerted"), two coupons (targeted and untargeted) model, and consumer
behavior statistics known to the retailer, we show that a stationary
threshold-based policy is the optimal coupon-offering strategy for a retailer
that wishes to minimize its expected discounted cost. The threshold is a
function of all model parameters; the retailer offers a targeted coupon if
their belief that the consumer is in the "Alerted" state is below the
threshold. We extend this two-state model to consumers with multiple
privacy-sensitivity states as well as coupon-dependent state transition
probabilities. Furthermore, we study the case with imperfect (noisy) cost
feedback from consumers and uncertain initial belief state.
