Undivide and Conquer: On Selling a Divisible and Homogeneous Good

Levy, Omer; Smorodinsky, Rann; Tennenholtz, Moshe

doi:10.1515/bejte-2014-0002

Cited by 1 publication

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References 15 publications

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“…In the economics literature, divisible items have received attention, with the focus being mostly on whether bundling can be beneficial or not [27] and on how to structure the sale as many auctions of shares [34]. Perfect divisibility is considered in [23,30]. In another more related direction, the operations research community has considered resource allocation mechanisms to divide an item based on signals received by the agents, that are further used to impose payments to the agents.…”

Section: Related Workmentioning

confidence: 99%

Simple posted pricing mechanisms for selling a divisible item

Caragiannis,

Kerentzis

2020

Preprint

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We study the problem of selling a divisible item to agents who have concave valuation functions for fractions of the item. This is a fundamental problem with apparent applications to pricing communication bandwidth or cloud computing services. We focus on simple sequential posted pricing mechanisms that use linear pricing, i.e., a fixed price for the whole item and proportional prices for fractions of it. We present results of the following form that can be thought of as analogs of the well-known prophet inequality of Samuel-Cahn (1984). For ρ ≈ 32%, if there is a linear pricing so that sequential posted pricing sells a ρ-fraction of the item, this results in a ρ-approximation of the optimal social welfare. The value of ρ can be improved to approximately 42% if sequential posted pricing considers the agents in random order. We also show that the best linear pricing yields an expected revenue that is at most O(κ 2 ) times smaller than the optimal one, where κ is a bound on the curvature of the valuation functions. The proof extends and exploits the approach of Alaei et al. ( 2019) and bounds the revenue gap by the objective value of a mathematical program. The dependence of the revenue gap on κ is unavoidable as a lower bound of Ω(ln κ) indicates.

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