DeepAI

# Static pricing for multi-unit prophet inequalities

We study a pricing problem where a seller has k identical copies of a product, buyers arrive sequentially, and the seller prices the items aiming to maximize social welfare. When k=1, this is the so called prophet inequality problem for which there is a simple pricing scheme achieving a competitive ratio of 1/2. On the other end of the spectrum, as k goes to infinity, the asymptotic performance of both static and adaptive pricing is well understood. We provide a static pricing scheme for the small-supply regime: where k is small but larger than 1. Prior to our work, the best competitive ratio known for this setting was the 1/2 that follows from the single-unit prophet inequality. Our pricing scheme is easy to describe as well as practical – it is anonymous, non-adaptive, and order-oblivious. We pick a single price that equalizes the expected fraction of items sold and the probability that the supply does not sell out before all customers are served; this price is then offered to each customer while supply lasts. This pricing scheme achieves a competitive ratio that increases gradually with the supply and approaches to 1 at the optimal rate. Astonishingly, for k<20, it even outperforms the state-of-the-art adaptive pricing for the small-k regime.

• 22 publications
• 5 publications
• 16 publications
01/19/2020

### Predict and Match: Prophet Inequalities with Uncertain Supply

We consider the problem of selling perishable items to a stream of buyer...
04/17/2023

### Optimal Pricing Schemes for Identical Items with Time-Sensitive Buyers

Time or money? That is a question! In this paper, we consider this dilem...
07/01/2021

### Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions

We consider the problem of posting prices for unit-demand buyers if all ...
07/19/2021

### Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes

We show that a competitive equilibrium always exists in combinatorial au...
12/10/2020

### Online Posted Pricing with Unknown Time-Discounted Valuations

We study the problem of designing posted-price mechanisms in order to se...
12/10/2019

### Graph Pricing with Limited Supply

We study approximation algorithms for graph pricing with vertex capaciti...
04/12/2022

### The Effects of Dynamic Learning and the Forgetting Process on an Optimizing Modelling for Full-Service Repair Pricing Contracts for Medical Devices

In order to improve the profitability and customer service management of...