[Paper Review] Pricing for online resource allocation: intervals and paths

Shuchi Chawla, J. Benjamin Miller+1 more|arXiv (Cornell University)|Jan 6, 2019

Auction Theory and Applications14 citations

TL;DR

This paper introduces static, anonymous bundle pricing mechanisms for online resource allocation with interval and path preferences, achieving sublogarithmic and nearly logarithmic competitive ratios respectively—representing exponential improvements over item pricing. The approach optimizes social welfare in settings with complementarities, with performance improving linearly with item supply.

ABSTRACT

We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the bundles are drawn from known distributions. This problem is closely related to the so-called prophet-inequality of Krengel and Sucheston [23] and its extensions in recent literature. Motivated by applications to cloud economics, we consider two kinds of buyer preferences. In the first, items correspond to different units of time at which a resource is available; the items are arranged in a total order and buyers desire intervals of items. The second corresponds to bandwidth allocation over a tree network; the items are edges in the network and buyers desire paths.Because buyers' preferences have complementarities in the settings we consider, recent constant-factor approximations via item prices do not apply, and indeed strong negative results are known. We develop static, anonymous bundle pricing mechanisms.For the interval preferences setting, we show that static, anonymous bundle pricings achieve a sublogarithmic competitive ratio, which is optimal (within constant factors) over the class of all online allocation algorithms, truthful or not. For the path preferences setting, we obtain a nearly-tight logarithmic competitive ratio. Both of these results exhibit an exponential improvement over item pricings for these settings. Our results extend to settings where the seller has multiple copies of each item, with the competitive ratio decreasing linearly with supply. Such a gradual tradeoff between supply and the competitive ratio for welfare was previously known only for the single item prophet inequality.

Motivation & Objective

• To design efficient pricing mechanisms for online resource allocation where buyers have complementarities in item bundles.
• To address settings where traditional item pricing fails due to complementarities, such as time-interval and tree-network path allocations.
• To achieve tight approximations to social welfare using static, anonymous bundle pricing in online settings with known buyer value distributions.
• To extend the tradeoff between supply and competitive ratio beyond single-item prophet inequalities.

Proposed method

• Develop static, anonymous bundle pricing mechanisms tailored to interval and path preferences in online resource allocation.
• Model buyer preferences as intervals of time-ordered items or paths in a tree network, with values drawn from known distributions.
• Use competitive ratio analysis to evaluate welfare approximation guarantees under online arrival of buyers.
• Prove that bundle pricing achieves sublogarithmic (interval) and nearly logarithmic (path) competitive ratios, improving upon item pricing.
• Analyze the impact of multiple item copies on the competitive ratio, showing a linear improvement with supply.
• Extend results to settings with multiple copies per item, demonstrating a gradual tradeoff between supply and competitive ratio.

Experimental results

Research questions

• RQ1 Can static, anonymous bundle pricing achieve better competitive ratios than item pricing in online resource allocation with complementarities?
• RQ2 What is the optimal competitive ratio achievable for interval preferences under online buyer arrivals with known value distributions?
• RQ3 How does bundle pricing perform for path preferences in tree-structured networks compared to item pricing?
• RQ4 Does increasing item supply lead to a linear improvement in the competitive ratio for bundle pricing mechanisms?
• RQ5 Can the results be extended to settings with multiple copies of each item while maintaining tight welfare approximations?

Key findings

• For interval preferences, static, anonymous bundle pricing achieves a sublogarithmic competitive ratio, which is optimal within constant factors among all online algorithms.
• For path preferences, the mechanism achieves a nearly-tight logarithmic competitive ratio, significantly improving upon item pricing.
• The competitive ratio for bundle pricing improves linearly with the number of available copies per item, extending a known tradeoff from single-item prophet inequalities.
• The results demonstrate an exponential improvement over item pricing in settings with complementarities.
• The mechanisms are truthful and do not require dynamic pricing or complex allocation rules, relying instead on static, anonymous bundle prices.
• The framework applies to practical applications such as cloud resource allocation, where buyers request time intervals or network paths.