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Non-zero sum game with priority as Dynkin’s game. (English) Zbl 0763.90095

The authors consider optimal stopping of a Markov chain by two participants. The first participant has a priority. Thus, he is free to choose his optimal stopping time. The second participant, however, is sometimes limited by the action taken by the first participant and can only optimize subject to this constraint. The authors show the relations between this problem and a non-zero sum Dynkin game. Based on these results the authors consider the secretary problem with two employers in which each applicant is reviewed by the first employer and, if not accepted by him, can be reviewed by the second employer. They solve several versions of this problem in which one of the employers wants to choose the best applicant and the other employer is satisfied by the best or second best applicant.
Reviewer: S.Gal (Haifa)

MSC:

90C40 Markov and semi-Markov decision processes
91A40 Other game-theoretic models
60G40 Stopping times; optimal stopping problems; gambling theory
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