Intermediary sets fair fixed prices for buying and selling limited goods
Balanced Posted Prices in Stationary Two-Sided Markets
Computer Science and Game Theory
Summary
This paper looks at a middleman who buys items from sellers and sells them to buyers, but can only store a limited number of items. The authors find prices that let the middleman trade efficiently over time without knowing future buyers or sellers. They balance how often items are bought and sold and ensure the profits are nearly as good as if the middleman knew everything in advance. Their methods work even when only one item can be stored for each kind and can be calculated fairly quickly.
What this means in practice
- •For ecommerce platform operators: Set fixed buy and sell prices to manage inventory while maintaining near-optimal trade efficiency in online marketplaces with uncertain arrivals.
- •For supply chain managers: Decide pricing policies to balance purchase and sales rates when storage capacity is limited, improving trading gains over time.
Authors
Ilan Reuven Cohen
Abstract
We study an intermediary that buys nonperishing items from arriving sellers and sells them to arriving buyers, subject to limited storage. Sellers and buyers arrive according to independent Poisson processes. The intermediary pays and charges the same fixed item prices, aiming to maximize long-run gains from trade: buyer value minus seller cost. Our benchmark may choose allocations directly, has unlimited storage, and must purchase each unit before allocating it. Its optimal long-run gain rate equals the value of a linear program of average purchase and allocation rates, with or without knowledge of future arrivals. For buyers whose bundle values are maxima of nonnegative additive valuations (XOS), we compute static common prices that guarantee half of this benchmark for arbitrary finite item capacities, even one storage slot per item, regardless of how ties are resolved without using future arrivals. The prices are computable in polynomial time using demand and supporting-value queries. The construction equalizes itemwise lower bounds on buyer and seller contributions to gains from trade, accounting for procurement costs. We call this contribution balance. As a single-item foundation, we also equalize the rates of purchases and sales selected by the price, before checking inventory availability. We call this rate balance. For capacity $C$, it yields the tight guarantee $C/(C+1)$. The two principles parallel proofs of the classical prophet inequality based on half the expected benchmark and on a median threshold, adapting these balancing ideas to recurring two-sided markets with limited inventory.