Odds -theorem and monotonicity

Bruss, F. Thomas

doi:10.14708/ma.v47i1.6481

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…It is easy to check that this monotonicity property is equivalent to the uni-modality property proved in Bruss [26] (p. 1386, lines 3-12), reference [27]. The latter implies that the optimal rule is a monotone rule in the sense that, once it is optimal to stop on a success at index k, then it is also optimal to stop on a success after index k. (For a convenient criterion for a stopping rule in the discrete setting being monotone, see also Ferguson [28] (p. 49)) .…”

Section: Randomly Delayed Stoppingmentioning

confidence: 83%

Combined Games with Randomly Delayed Beginnings

Bruss

2021

Mathematics

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This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

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Section: Randomly Delayed Stoppingmentioning

confidence: 83%

Combined Games with Randomly Delayed Beginnings

Bruss

2021

Mathematics

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A note on last-success-problem

Ribas

2021

Theor. Probability and Math. Statist.

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A unified approach for solving sequential selection problems

Goldenshluger¹,

Malinovsky²,

Zeevi³

2020

Probab. Surveys

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In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as random problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.

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Odds -theorem and monotonicity

Cited by 4 publications

References 11 publications

Combined Games with Randomly Delayed Beginnings

Combined Games with Randomly Delayed Beginnings

A note on last-success-problem

A unified approach for solving sequential selection problems

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