Efficient Algorithms for Learning Revenue-Maximizing Two-Part Tariffs

IJCAI 2020, pp. 332-338, 2020.

Cited by: 0|Bibtex|Views38|DOI:https://doi.org/10.24963/ijcai.2020/47
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We study learning high-revenue menus of two-part tariffs from buyer valuation data, in the setting where the mechanism designer has access to samples from the distribution over buyers' values rather than an explicit description thereof

Abstract:

A two-part tariff is a pricing scheme that consists of an up-front lump sum fee and a per unit fee. Various products in the real world are sold via a menu, or list, of two-part tariffs---for example gym memberships, cell phone data plans, etc. We study learning high-revenue menus of two-part tariffs from buyer valuation data, in the setti...More

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Introduction
  • A two-part tariff (TPT) consists of an up-front lump sum fee p1 and a fee p2 for every additional unit purchased.
  • Keurig sells coffee machines that require proprietary coffee pods.
  • Another example is health club memberships, where participants often are required to pay an up-front fixed membership fee, as well as a monthly fee.
  • ) of L TPTs, and a buyer may elect to pay according to any one of the L TPTs. Menus of TPTs are prevalent: health clubs, amusement parks, wholesale stores like Costco, cell phone companies, and credit card companies all frequently offer various tiers of membership usually consisting of lower future payments for a larger up-front payment
Highlights
  • A two-part tariff (TPT) consists of an up-front lump sum fee p1 and a fee p2 for every additional unit purchased
  • We study the case where each buyer belongs to one of M markets, in which case a two-part tariff pricing scheme is of the form (p1, . . . , pM ), where buyers in market m are offered menu pm
  • We prove how many samples suffice to guarantee that a two-part tariff scheme that is feasible on the samples is feasible on a new problem instance with high probability
  • In this paper we studied efficient algorithms for finding revenue-maximizing two-part tariff pricing schemes in the setting where the buyers’ valuation distributions are given via samples
  • These algorithms have clear direct uses. They provide the missing piece in the recent generalization theory for two-part tariff [Balcan et al, 2018], which uses samples of valuations as the input, and whose generalization approach is based on revenue-maximizing two-part tariff schemes, but which did not provide any algorithms for computing such schemes
  • We presented an algorithm for optimizing length-L menus of two-part tariff with complexity exponential only in L and polynomial in the other problem parameters
Conclusion
  • Conclusions and Future Research

    TPTs are a frequently-used pricing scheme in many applications.
  • In this paper the authors studied efficient algorithms for finding revenue-maximizing TPT pricing schemes in the setting where the buyers’ valuation distributions are given via samples.
  • These algorithms have clear direct uses.
  • The authors presented an algorithm for optimizing length-L menus of TPTs with complexity exponential only in L and polynomial in the other problem parameters
Summary
  • Introduction:

    A two-part tariff (TPT) consists of an up-front lump sum fee p1 and a fee p2 for every additional unit purchased.
  • Keurig sells coffee machines that require proprietary coffee pods.
  • Another example is health club memberships, where participants often are required to pay an up-front fixed membership fee, as well as a monthly fee.
  • ) of L TPTs, and a buyer may elect to pay according to any one of the L TPTs. Menus of TPTs are prevalent: health clubs, amusement parks, wholesale stores like Costco, cell phone companies, and credit card companies all frequently offer various tiers of membership usually consisting of lower future payments for a larger up-front payment
  • Conclusion:

    Conclusions and Future Research

    TPTs are a frequently-used pricing scheme in many applications.
  • In this paper the authors studied efficient algorithms for finding revenue-maximizing TPT pricing schemes in the setting where the buyers’ valuation distributions are given via samples.
  • These algorithms have clear direct uses.
  • The authors presented an algorithm for optimizing length-L menus of TPTs with complexity exponential only in L and polynomial in the other problem parameters
Funding
  • This material is based on work supported by the NSF under grants IIS-1718457, IIS-1617590, IIS-1901403, CCF1733556, CCF-1535967, CCF-1910321, and SES-1919453, the ARO under award W911NF-17-1-0082, the Defense Advanced Research Projects Agency under cooperative agreement HR0011202000, an AWS Machine Learning Research Award, an Amazon Research Award, a Bloomberg Research Grant, and a Microsoft Research Faculty Fellowship
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