Online computation and competitive analysis
Online computation and competitive analysis
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
Sequential item pricing for unlimited supply
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Competitive algorithms for online pricing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
A global characterization of envy-free truthful scheduling of two tasks
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Envy-Free Makespan Approximation
SIAM Journal on Computing
Online pricing for multi-type of items
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Online pricing for bundles of multiple items
Journal of Global Optimization
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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 use a novel general technique.