Optimal stopping problems by two or more decision makers: a survey

Abdelaziz, Fouad Ben; Krichen, Saoussen

doi:10.1007/s10287-006-0029-5

Cited by 24 publications

(15 citation statements)

References 36 publications

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“…This class of problems have been referred to as expected rank SPs (ERSP), and form the basis of the present study. Theoretical extensions of the SP to committee search are more recent (see e.g., Sakaguchi andMazalov 2004, Abdelaziz andKrichen 2007). They predominantly focus on two-person committees.…”

Section: The Secretary Problem (Sp) As a Theoretical Paradigmmentioning

confidence: 99%

“…As in the classical SP, we assume that every member can rank-order the n alternatives in terms of their desirability (1 = best, 2 = second best, etc.) with no ties, so that when the committee is inspecting the j-th alternative every member i (indexed by i = 1, 2, … m) has a well-defined Lindley (1961), Freeman (1983), Samuels (1991), Stein et al (2003), Bearden et al (2006) Classical best choice SP (BCSP) models Chow et al (1964) Expected rank SP (ERSP) model Not applicable Sakaguchi and Mazalov (2004), Abdelaziz and Krichen (2007) Committee search extensions; predominantly two-person committees…”

Section: Individual Preferencesmentioning

confidence: 99%

“…Instead, she may only be able to make ordinal preference comparisons over the inspected alternatives. Those situations pertain to the no-information or partial-information case (e.g., Abdelaziz andKrichen 2007, Mak, Rapoport, andSeale 2014), where only the rank of each alternative, once it is inspected, may be determined during the search relative to the ranks of all the alternatives that have been inspected and subsequently rejected.…”

Section: Introductionmentioning

confidence: 99%

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Voting Rules in Sequential Search by Committees: Theory and Experiments

et al. 2019

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We propose a committee extension of the individual sequential search model called the “secretary problem,” where collective decisions on when to stop the search are reached via a prespecified voting rule. We offer a game-theoretic analysis of our model and then report two experiments on three-person committees with either uncorrelated or perfectly correlated preferences under three different voting rules followed by a third experiment on single decision makers. Relative to equilibrium predictions, committees with uncorrelated preferences oversearched under minority and majority voting rules but, otherwise, undersearched or approximated equilibrium play. Individually, committee members were often less strategic when their preferences were uncorrelated than when they were perfectly correlated. Collectively, committees’ decisions were more strategic than single decision makers’ only under the unanimity rule, although still not significantly better in terms of the decision makers’ welfare. Finally, across our experiments that involved committee search, the unanimity rule always optimized committee welfare. This paper was accepted by Yan Chen, behavioral economics.

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Section: The Secretary Problem (Sp) As a Theoretical Paradigmmentioning

confidence: 99%

Section: Individual Preferencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Voting Rules in Sequential Search by Committees: Theory and Experiments

et al. 2019

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“…By this paper, we try to recall the model and result to emphasize the role of Larry Shepp in creation of this part of interesting modeling of decision makers' behavior, as well as to draw attention to the authors of contemporary reports on further considerations of this kind (cf. Ben Abdelaziz and Krichen (), Adell and Alzer ()). It will be an interesting task to compare various information models in the related problems investigated by Sakaguchi (), Ano (), Szajowski (, ), Ramsey and Szajowski () and Ramsey (, ).…”

Section: Introductionmentioning

confidence: 99%

On multilateral incomplete information decision models

Szajowski

Skarupski

2019

High Frequency

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This paper treats the decision problem related to theobservation of a Markov process by decision makers. The informationdelivered to the players is based on the aggregation of thehigh‐frequency data by some functions. Admissible strategies arestopping moments related to the available information. The paymentsare defined by the state at the time of stopping. The players' decision to stop has various effects which depend on the decisionmakers' type. The type β player's stopping decision assignsthe state of the process with chance β, and it offers thisstate to the opponent with probability 1-β. The knowledgeabout the type of the players is not public and in this way, thepayers have also different information. The details of thedescription allow to formulate the problem as a Bayesian game withsets of strategies based on the stopping times. It is an extensionof Dynkin's game related to the observation of a Markov process withthe random assignment mechanism of states to the players. Some examples related to the best choice problem (BCP) are analyzed. MSC (2000) Primary: 90D15; Secondary: 93C30.

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“…The aggregation weights are updated from step to step depending on previous situations of the decision process. A survey of the optimal stopping problem including two DMs with its various definitions and solution approaches was proposed in Ben Abdelaziz and Krichen (2007).…”

Section: Introductionmentioning

confidence: 99%

An Optimal Stopping Problem with Two Decision Makers

Krichen

Abdelaziz

2007

Sequential Analysis

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We investigate in this paper an optimal stopping problem where two decision makers are involved in the selection of a single offer. Suppose that n offers are examined one at a time by both decision makers. At each stage, a decision must be taken: accept the current offer and stop the selection process, or discard it and examine the next offer. We assume that no recall of previously examined offers is allowed. A conflict arises when one decision maker decides to accept a currently inspected offer and the second decides to discard it. In such conflicting situations, a decision should be taken by defining a stopping rule for the group. We propose to stop the process if either decision maker accepts an offer. We develop the dynamic programming approach for this problem and state the optimal strategy for a fixed utility. Then, we propose an experimental investigation of the problem.

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Optimal stopping problems by two or more decision makers: a survey

Abstract: Dynamic programming, Game theory, Group decisions, Optimal stopping,

Cited by 24 publications

References 36 publications

Voting Rules in Sequential Search by Committees: Theory and Experiments

Voting Rules in Sequential Search by Committees: Theory and Experiments

On multilateral incomplete information decision models

An Optimal Stopping Problem with Two Decision Makers

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