  We propose a new Markov Decision Process (MDP) model for ad auctions to
capture the user response to the quality of ads, with the objective of
maximizing the long-term discounted revenue. By incorporating user response,
our model takes into consideration all three parties involved in the auction
(advertiser, auctioneer, and user). The state of the user is modeled as a
user-specific click-through rate (CTR) with the CTR changing in the next round
according to the set of ads shown to the user in the current round. We
characterize the optimal mechanism for this MDP as a Myerson's auction with a
notion of modified virtual value, which relies on the value distribution of the
advertiser, the current user state, and the future impact of showing the ad to
the user. Leveraging this characterization, we design a sample-efficient and
computationally-efficient algorithm which outputs an approximately optimal
policy that requires only sample access to the true MDP and the value
distributions of the bidders. Finally, we propose a simple mechanism built upon
second price auctions with personalized reserve prices and show it can achieve
a constant-factor approximation to the optimal long term discounted revenue.
