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Over the past decade, an exciting connection has developed between the theory of posted-price mechanisms and the prophet inequality, a result from the theory of optimal stopping. This survey provides an overview of this literature, covering extensions and applications of the prophet inequality through the lens of an economic proof of this classic result. We focus on highlighting ways in which the economic perspective drives new advances in the theory of online stochastic optimization, and vice versa.
Brendan Lucier (Mon,) studied this question.