Expectation Inequalities Associated with Prophet Problems
نویسنده
چکیده
Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of order selection, non-measurable stop rules, look-ahead stop rUles, and iterated maps of random variables. Also, proofs are given of two results of Hill and Hordijk c?ncerning optimal orderings of uniform and exponential d~stributions. §l. INTRODUCTION Universal inequalities comparing the two func
منابع مشابه
A Survey of Prophet Inequalities in Optimal Stopping Theory
The Illain purpose of this paper is to provide a brief survey of what has CODle to be known as "prophet inequalities" or ~~prophet problerns" in the t heory of optirnal stopping. rrhis survpy includes surnrnaries of the basic results, subs e quent extensioIls and variations of these results, Blain proof tools an d techniques (with concrete exarllples), a,ad a list of open problenls. Although t...
متن کاملProphet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards V1, ..., Vn and must decide, for each reward Vi, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value Vi. The gambler’s goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have be...
متن کاملAutomated Online Mechanism Design and Prophet Inequalities
Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many real-worl...
متن کاملMatroid Prophet Inequalities and Bayesian Mechanism Design
Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel, Sucheston, and Garling asserts that a gambler who knows the distribution of each random variable can achieve at least half as much reward, in expectation, as a "pr...
متن کاملPolymatroid Prophet Inequalities
Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once. The goal of both is to decide on fractions of each number they want to keep so as to maximize the weighted fractional sum of the numbers chosen. The classic result of Krengel and Sucheston (1977-78) asserts th...
متن کامل