How well can Priceline sell airline tickets ?

We consider the following simple model for how Priceline sets airline prices. Assume Priceline wants to sell tickets for a single flight (which are assumed to have unlimited supply) over (discrete) time. Each bidder submits a triple (s, e, b) where s is the time when the bidder will arrive, e is the time when the bidder will leave and b is the maximum amount the bidder is willing to pay for a ticket (every bidder is interested in only one ticket). On each day t, Priceline sets a price p(t) and every bidder buys a ticket on the first day t (at price p(t)) such that p(t) is less than or equal to its bid value and t is between its arrival and departure time. The goal for the Priceline is to set prices so as to maximize its revenue. We also consider a related model studied by Guruswami et al. [1], where each bidder buys the ticket at the minimum price p(t) (provided it is at most b) where t is between its arrival and departure time. We study the above optimization problems in both the offline and online settings. We show that the offline algorithm can be solved exactly in polynomial time. We also give upper and lower bounds for online algorithms (both deterministic and randomized) for this problem.