Some Bilateral Approach to the Generalized Secretary Problem
Krzysztof Szajowski · 1992
Two employers, Player 1 and Player 2, are to view sequentially a group of N applicant for vacancies in their enterprise. The aim of the players is to accept the best or the second best (BOS) applicant but better than another player. Their decisions are based on relative ranks of applicants and previous decisions of the opponent. If the applicant is viewed the employer must either accept or reject her. The applicant once accepted cannot be rejected, once rejected cannot be reconsidered. Each employer can accept at most one applicant. When both players want to accept the same applicant the priority is given to Player 1. The considered problem is a game variant of the double choice problem (see [5] for a review) and a generalization of the priority game approach to the generalized secretary problem [4], [6], [7]. This model and other game approaches to the problem differs in, among others, the structure of payoff functions. It is the first example in which the gain of both players depends on the candidates accepted by the opponent. The formal model of the problem is given and the numerical solution of the problem posed is presented. The most relevant game model has been investigated by Ano [1]. The aim of the players in his model is to choose BOS but when one player stops another one cannot choose any other object.