  We provide a characterization of revenue-optimal dynamic mechanisms in
settings where a monopolist sells k items over k periods to a buyer who
realizes his value for item i in the beginning of period i. We require that the
mechanism satisfies a strong individual rationality constraint, requiring that
the stage utility of each agent be positive during each period. We show that
the optimum mechanism can be computed by solving a nested sequence of static
(single-period) mechanisms that optimize a tradeoff between the surplus of the
allocation and the buyer's utility. We also provide a simple dynamic mechanism
that obtains at least half of the optimal revenue. The mechanism either ignores
history and posts the optimal monopoly price in each period, or allocates with
a probability that is independent of the current report of the agent and is
based only on previous reports. Our characterization extends to multi-agent
auctions. We also formulate a discounted infinite horizon version of the
problem, where we study the performance of "Markov mechanisms."
