are well known in the Middle East, where I did a part of my Ph.D. thesis in the 1990s.
However, probability theory rather been interested in so-called "prophet inequalities", and I published a series of articles on this topic (the last appeared in 2017, see below).
Essentially, there is a certain well-defined mathematical situation, and two "persons" with different levels of information - the statistician and the prophet. Both would like to maximize their expected returns S and P, respectively.
The statistician makes successive observations and thus knows the past (up to now). The prophet, however, knows past and future. Thus, quite obviously, the latter is better off (S ≤ P). Prophet inequalities go much farther. For example, a classic and quite typical result says that P ≤ 2 S. In other words, the expected return to the prophet (P) is bounded, it cannot exceed a certain threshold, e.g., twice the statistician's value (2S).
Saint-Mont, U. 'Comparing different information levels.' The Open Statistics & Probability Journal, 2017, 8, 7-18.
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