Prices, Auctions, and Combinatorial Prophet Inequalities
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The most common way to sell resources, from apples to business licenses to concert tickets, is to post prices. A choice of prices can be viewed as an algorithm for an online stochastic optimization problem, which makes decisions using value thresholds. This connection provides an opportunity to use the famous prophet inequality -- which describes the power of threshold rules -- to study pricing problems, and vice-versa. In this talk I'll present a general framework for deriving new prophet inequalities using economic insights from pricing, with algorithmic applications. Along the way, I'll describe an unexpected connection between posted prices and equilibria of non-truthful auctions.