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How well can Priceline set airline ticket prices ? N. Bansal, N. Chen, N. Cherniavsky, A. Rudra, B. Schieber, M. Sviridenko

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Example $ 50 $250 $200 $150 $100 MonTue Wed ThuFriSat Revenue: 200 400 50 Price: 100 20050 // = 650

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Example (cont.) $ 50 $250 $200 $150 $100 MonTue Wed ThuFriSat Revenue: 200 250 200 Price: 100 25050 // = 700 200 50

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The Model Each day a collection of customers arrives and each of those customers submits a bid value b : the maximum amount that the customer is willing to pay for a ticket. after which the customer is no longer willing to buy the ticket. Each customer has an expiration time : after which the customer is no longer willing to buy the ticket.

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The Model (cont.) Priceline sets a single price p(t) every day for the ticket. Custom buys a ticket at the first price p(t), such that p(t) b, where t is between the arrival time and expiration time of the customer. The goal of Priceline is to earn as much money as possible (we call this PL-model).

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Competitive Analysis Competitive analysis: compare the solution of the algorithm A with the optimal offline solution. Metric: optimal offline solution Competitive ratio = max b OPT offline (b) / Revenue A (b)

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Goal of this work Goal is to design algorithms for Priceline Maximizes revenue Offline case Polynomial time algorithm The general case Algorithm that minimize the competitive ratio

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Results OfflineOnline PL-model DeterministicRandomized Polytime O(log h) (log h) 1/2 ) O(loglog h) (loglog h) 1/2 ) Where h denotes the ratio of max to min bid value

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Open Problems OfflineOnline PL-model DeterministicRandomized Polytime O(log h) (log h) 1/2 ) O(loglog h) (loglog h) 1/2 ) Reduce the gap between upper and lower bounds

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Open questions What about game theory versions Assumed that all customers tell their true bid values How to do pricing in presence of selfish customers?

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