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TL;DR#
Selling a single item to multiple buyers with unknown private valuations is a common economic problem. Posted pricing, where the seller sets a fixed price for each buyer, is a simple and practical approach, but finding optimal prices requires knowledge of buyer valuations. Previous work primarily focused on independent buyer valuations; this paper tackles the more realistic but complex scenario where buyer valuations can be correlated. It also examines both welfare maximization (best overall outcome) and revenue maximization (highest revenue for the seller).
This paper addresses the sample complexity problem, essentially answering the question of “how many buyer valuations do we need to sample to get near optimal prices?” It provides matching upper and lower bounds on the number of samples needed for various settings (independent/correlated distributions, welfare/revenue maximization). The results show a significant difference between welfare and revenue maximization, and that correlation among buyer valuations changes the relationship between sample size and optimal pricing.
Key Takeaways#
Why does it matter?#
This paper is crucial because it bridges the gap in understanding sample complexity for posted pricing, a widely used mechanism in online markets. Its findings directly impact the design of efficient pricing strategies, particularly in the context of online auctions and dynamic pricing. The tight bounds derived provide practical guidelines for businesses and researchers, while the exploration of correlated distributions expands the theoretical understanding beyond traditional assumptions.
Visual Insights#
Full paper#
