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Polymatroid Prophet Inequalities
[article]
2013
arXiv
pre-print
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 that if both the gambler and the prophet can pick one number, then the gambler can do at least half as
arXiv:1307.5299v1
fatcat:ilmx6de6afduleu3mpmjkrbgsi