Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching

The two-envelope problem (or exchange problem) is one of maximizing the payoff in choosing between two values, given an observation of only one. This paradigm is of interest in a range of fields from engineering to mathematical finance, as it is now known that the payoff can be increased by exploiting a form of information asymmetry. Here, we consider a version of the 'two-envelope game' where the envelopes’ contents are governed by a continuous positive random variable. While the optimal switching strategy is known and deterministic once an envelope has been opened, it is not necessarily optimal when the content's distribution is unknown. A useful alternative in this case may be to use a switching strategy that depends randomly on the observed value in the opened envelope. This approach can lead to a gain when compared with never switching. Here, we quantify the gain owing to such conditional randomized switching when the random variable has a generalized negative exponential distribution, and compare this to the optimal switching strategy. We also show that a randomized strategy may be advantageous when the distribution of the envelope's contents is unknown, since it can always lead to a gain.Mark D. McDonnell, Alex J. Grant, Ingmar Land, Badri N. Vellambi, Derek Abbott and Ken Leve

The two-envelope problem revisited

The two-envelope problem has intrigued mathematicians for decades, and is a question of choice between two states in the presence of uncertainty. The problem so far, is considered open and there has been no agreed approach or framework for its analysis. In this paper we outline an elementary approach based on Cover's switching function that, in essence, makes a biased random choice where the bias is conditioned on the observed value of one of the states. We argue that the resulting symmetry breaking introduced by this process results in a gain counter to naive expectation. Finally, we discuss a number of open questions and new lines of enquiry that this discovery opens up. © 2010 World Scientific Publishing Company.Derek Abbott, Bruce R. Davis and Juan M. R. Parrond

Studying the Prediction of Spontaneous Preterm Birth Using Quantitative Fetal Fibronectin (fFN) for Threatened Preterm Labor: A Pilot Study.

Objective To determine whether the quantitative value of fetal fibronectin (fFN) can predict preterm birth (PTB) in women with Threatened Preterm Labor. Design A retrospective study carried out in WWRC between the years 2017-2022. Method A total of 94 patients were selected, all of which had a fFN test and were admitted at 24-33 weeks of gestational age. Concentration of fFN was divided into 5 categories: ≤10, 11-49, 50-199, 200-499 and ≥500ng/mL. A concentration of ≥50ng/mL was classified as a positive test and used as an international cutoff value. Results A total of 31 women had a fFN value of ≤10ng/mL; of these, 23 (74.19%) delivered term birth (TB) (≥37 weeks of gestational age), with a mean of 10 and a range of 4-14 delivery weeks following fFN testing (m:10, r:4-14), whilst 8 (25.8%) delivered a preterm birth ( Conclusion Our preliminary data showed that the quantitative value of fFN alone is insufficient to determine PTB. Other factors should be considered such as cervical length, history of PTB, uterine surgeries, PPROM, and more. It is important to consider the etiology of PTB and apply fFN in cases where the test will benefit. The low PPV and NPV could be attributed to small sample size, therefore a larger study is needed to confirm the findings.  </p