Online computation and competitive analysis
Online computation and competitive analysis
Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Adaptive limited-supply online auctions
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Online learning in online auctions
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Online auctions with re-usable goods
Proceedings of the 6th ACM conference on Electronic commerce
Online ascending auctions for gradually expiring items
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Envy-free makespan approximation: extended abstract
Proceedings of the 11th ACM conference on Electronic commerce
Theoretical Computer Science
Frequency capping in online advertising
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Equilibrium pricing with positive externalities
Theoretical Computer Science
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We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the item, and a maximum value the bidder is willing to pay for the item. On every time unit the seller sets a price for the item. The seller's goal is to set the prices so as to maximize revenue from the sale of copies of items over the time period. In the first model considered we assume that all bidders are impatient, that is, bidders buy the item at the first time unit within their bid interval that they can afford the price. To the best of our knowledge, this is the first work that considers this model. In the offline setting we assume that the seller knows the bids of all the bidders in advance. In the online setting we assume that at each time unit the seller only knows the values of the bids that have arrived before or at that time unit. We give a polynomial time offline algorithm and prove upper and lower bounds on the competitiveness of deterministic and randomized online algorithms, compared with the optimal offline solution. The gap between the upper and lower bounds is quadratic. We also consider the envy free model in which bidders are sold the item at the minimum price during their bid interval, as long as it is not over their limit value. We prove tight bounds on the competitiveness of deterministic online algorithms for this model, and upper and lower bounds on the competitiveness of randomized algorithms with quadratic gap. The lower bounds for the randomized case in both models uses a novel general technique.