A non-zero-sum no-information best-choice game

Minoru Sakaguchi () and Vladimir V. Mazalov ()

Mathematical Methods of Operations Research, 2004, vol. 60, issue 3, 437-451

Abstract: A given number of n applicants are to be interviewed for a position of secretary. They present themselves one-by-one in random order, all n! permutations being equally likely. Two players I and II jointly interview the i-th applicant and observe that his (or her) relative rank is y for I and z for II, relative to i−1 applicants that have already seen (rank 1 is for the best). Each player chooses one of the two choices Accept or Reject. If choice-pair is R-R, then the i-th is rejected, and the players face the next i+1-th applicant. If A-A is chosen, then the game ends with payoff to I (II), the expected absolute rank under the condition that the i-th has the relative rank y (z). If players choose different choices, then arbitration comes in, and forces players to take the same choices as I’s (II’s) with probability [InlineMediaObject not available: see fulltext.] Arbitration is fair if p=1/2. If all applicants except the last have been rejected, then A-A should be chosen for the last. Each player aims to minimize the expected payoff he can get. Explicit solution is derived to this n stage game, and numerical results are given for some n and p. The possibility of an interactive approach in this selection problem is analyzed. Copyright Springer-Verlag 2004

Keywords: Secretary problem; Optimal selection; Optimal stopping game; Equilibrium values; Interactive approach (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s001860400366

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