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Bilateral sequential games related to the no-information secretary problem. (English) Zbl 0549.90102

Summary: This paper considers a bilateral sequential game related to the classical secretary problem. Two players I and II jointly interview exactly n applicants (say, girls) for a secretarial position. Each girl is presented sequentially and radomly, and she is faced first to I’s choice, if he has not already made an acceptance. If I rejects, this girl is faced to II’s choice, if II has not already made on acceptance. Each player is allowed exactly one acceptance without recall to past decision stages. Each player is rewarded by \(+1\) (-1), if he accepts a girl who is (isn’t) absolutely best. The objective for I (II) in the game is to maximize (minimize) the expected payoff to I.
The optimal policies for the players and the value of the game are derived for the two cases where the payoffs are defined differently. Moreover, two types of related unsolved problems are mentioned.

MSC:

91A15 Stochastic games, stochastic differential games
91A05 2-person games
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