  A number of products are sold in the following sequence: First a focal
product is shown, and if the customer purchases, one or more ancillary products
are displayed for purchase. A prominent example is the sale of an airline
ticket, where first the flight is shown, and when chosen, a number of
ancillaries such as cabin or hold bag options, seat selection, insurance etc.
are presented. The firm has to decide on a sale format -- whether to sell them
in sequence unbundled, or together as a bundle -- and how to price the focal
and ancillary products, separately or as a bundle. Since the ancillary is
considered by the customer only after the purchase of the focal product, the
sale strategy chosen by the firm creates an information and learning dependency
between the products: for instance, offering only a bundle would preclude
learning customers' valuation for the focal and ancillary products
individually. In this paper we study learning strategies for such focal and
ancillary item combinations under the following scenarios: (a) pure unbundling
to all customers, (b) personalized mechanism, where, depending on some observed
features of the customers, the two products are presented and priced as a
bundle or in sequence, (c) initially unbundling (for all customers), and switch
to bundling (if more profitable) permanently once during the horizon. We design
pricing and decisions algorithms for all three scenarios, with regret upper
bounded by $O(d \sqrt{T} \log T)$, and an optimal switching time for the third
scenario.
