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

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

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

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

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.

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).

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)

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

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

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

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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