| Summary: | 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 its 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.
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