WINE 2015: Web and Internet Economics pp 1-15

# Sequential Posted Price Mechanisms with Correlated Valuations

• Allan Borodin
• Diodato Ferraioli
• Bart de Keijzer
• Stefano Leonardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)

## Abstract

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to the ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a $$\varOmega (1/\max \{1,d\})$$ fraction of the optimal revenue can be extracted, where d denotes the “degree of dependence” of the valuations, ranging from complete independence ($$d=0$$) to arbitrary dependence ($$d = n-1$$). When we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i, we prove that a constant fraction $$(2 - \sqrt{e})/4 \approx 0.088$$ of the optimal revenue can be always extracted.

## Notes

### Acknowledgments

We thank Joanna Drummond, Brendan Lucier, Tim Roughgarden and anonymous referees for their constructive comments.

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## Authors and Affiliations

• 1
• Allan Borodin
• 2
• Diodato Ferraioli
• 3
• Bart de Keijzer
• 1
• Stefano Leonardi
• 1
1. 1.Sapienza University of RomeRomeItaly