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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 Price: 100 200 50 // $250 // $200 // $150 // $100 $ 50 // Mon Tue Thu Fri Sat Wed Revenue: 200 = 650 50 400
Example (cont.) Price: 100 250 200 50 // $250 // $200 // $150 // $100 $ 50 // Mon Tue Thu Fri Sat Wed Revenue: 200 50 = 700 200 250
The Model • Each day a collection of customers arrives and each of those customers submits a bid valueb : the maximum amount that the customer is willing to pay for a 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 pricep(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 = maxbOPToffline(b) / RevenueA(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 Deterministic Randomized O(log h) O(loglog h) Polytime ((log h)1/2) ((loglog h)1/2) Where h denotes the ratio of max to min bid value
Open Problems Deterministic Randomized O(log h) O(loglog h) Polytime ((log h)1/2) ((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?