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Jose Correa: Prophet inequalities and posted price mechanisms: Part 1

Abstract: Posted price mechanisms (PPM) constitute an appealing and simple type of mechanism and has received a lot of attention in recent years. In this context,the seller simply makes take-it-or-leave-it offers to a set of buyers, and therefore strategic behavior vanishes. These mechanisms are closely connected to the theory of optimal stopping, and the so called prophet inequalities. In this first talk we will cover some of the basic results of this theory and see how it applies to that of PPMs. Furthermore, we will present a recent reduction that transforms any threshold stopping rule for a prophet inequality into a PPM. With this reduction at hand we will see how results for one of these problems leads to results in the other.