Abstract
In this paper we consider online auctions with buyback; a form of auctions where bidders arrive sequentially and the bidders have to be accepted or rejected immediately. Each bidder has a valuation for being allocated the good and a preemption price. Sold goods can be bought back from the bidders for a preemption price. We allow unbounded valuations and preemption prices independent from each other. We study the clairvoyant model, a model sitting between the traditional offline and online models. In the clairvoyant model, a sequence of all potential customers (their bids and compensations) is known in advance to the seller, but the seller does not know when the sequence stops. In the case of a single good, we present an algorithm for computing the difficulty \(\varDelta \), the optimal ratio between the clairvoyant mechanism and the pure offline mechanism (which knows when the sequence stops, and can simply sell the good to the customer with the highest bid, without having to pay any compensations). We also present an optimal clairvoyant mechanism if there are multiple goods to be sold. If the number of goods is unbounded, however, we show that the problem in the clairvoyant model becomes \(\mathcal {NP}\)-hard. Based on our results in the clairvoyant model, we study the \(\varDelta \)-online problem (where the sequence is unknown to the mechanism, but the difficulty \(\varDelta \) of the input sequence is known). We show that there is a tight gap of \(\varTheta (\varDelta ^5)\) between the offline and the online model.
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Notes
- 1.
In reality, airlines do not implement online auctions in the clean form described in this paper. Airlines do not seem to maximize their profits with this mechanism, probably for psychological reasons. As such, on web pages, flights still can be sold out, instead of just asking for a higher and higher premium for an unexpectedly popular flight.
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Brandes, P., Huang, Z., Su, HH., Wattenhofer, R. (2016). Clairvoyant Mechanisms for Online Auctions. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_1
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