F. Thomas Bruss

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Let X1, X2, . . . , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk sequentially and must stop on exactly one of them. No recollection of the preceding observations is permitted. What stopping rule τ minimizes the expected rank of the selected observation? This full-information expected-rank problem is known(More)
Let X1,X2, . . . ,Xn be i.i.d. random variables with a known continuous distribution function. Robbins’ problem is to find a sequential stopping rule without recall which minimizes the expected rank of the selected observation. An upper bound (obtained by memoryless threshold rules) and a procedure to obtain lower bounds of the value are known, but the(More)
Let X1, X2, . . . , Xn be independent random variables uniformly distributed on [0, 1]. We observe these sequentially and have to stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation? What is the value of the expected rank (as a function of n) and what is(More)
Two decision-makers A and B observe sequentially a given permutation of n uniquely rankable options. A and B have one choice each (without recall) and both must make a choice. At each step only the relative ranks are known, and A has the priority of choice. At the end the (absolute) ranks are compared and the winner is the one who has chosen the better(More)
We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final)(More)
Consider N balls that are distributed among V urns according to some distribution G. We do not see the outcome and now have to place one ball into one urn with the goal of maximizing the probability that it will be the left-most urn containing a single ball. How should we proceed? This is the urn-model translation of an interesting problem posed by an(More)