We study an extension of the unit-demand pricing problem in which the seller may offer bundles of items. If a customer buys such a bundle she is guaranteed to get one item out of it, but the seller does not make any promises of how this item is selected. This is motivated by the sales model of retailers like hotwire.com, which offers bundles of hotel rooms based on location and rating, and only identifies the booked hotel after the purchase has been made.
As the selected item is known only in hindsight, the buying decision depends on the customer’s belief about the allocation mechanism. We study strictly pessimistic and optimistic customers who always assume the worst-case or best-case allocation mechanism relative to their personal valuations, respectively. While the latter model turns out to be equivalent to the pure item pricing problem, the former is fundamentally different, and we prove the following results about it: (1) A revenue-maximizing pricing can be computed efficiently in the uniform version, in which every customer has a subset of items and the same non-zero value for all items in this subset and a value of zero for all other items. (2) For non-uniform customers computing a revenue-maximizing pricing is APX-hard. (3) For the case that any two values of a customer are either identical or differ by at least some constant factor, we present a polynomial time algorithm that obtains a constant approximation guarantee.
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