CDAM: Computational, Discrete and Applicable Mathematics@LSE

 CDAM Research Report, LSE-CDAM-2008-03

April 2008

Analysis and Design of Selection Committees: A Game Theoretic Secretary Problem

Steve Alpern and Shmuel Gal

Firms often delegate important decisions to committees which are set up specically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evalutions of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firms utility.

Our committee game has a first round in which the members sequentially, by order of player number, say `yea' or `nea' to the candidate. If there are sufficient `yeas' then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates.

Keywords: committee, stochastic game, voting, veto

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