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Optimal Pricing Schemes for an Impatient Buyer

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  • Yuan Deng
  • Jieming Mao
  • Balasubramanian Sivan
  • Kangning Wang

Abstract

A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time $T$, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms. I.e., mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer's value distribution.

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  • Yuan Deng & Jieming Mao & Balasubramanian Sivan & Kangning Wang, 2021. "Optimal Pricing Schemes for an Impatient Buyer," Papers 2106.02149, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2106.02149
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    References listed on IDEAS

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    Cited by:

    1. Yotam Gafni & Aviv Yaish, 2022. "Discrete & Bayesian Transaction Fee Mechanisms," Papers 2210.07793, arXiv.org, revised May 2024.

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