A sequential selection game with vetoes

We study an on-line selection game between two committee members (the players). The committee interviews candidates sequentially and has to decide, after each interview, whether to hire or to interview the next candidate.. Each player can either accept or reject the candidate, and if he rejects the candidate while the other accepts her, he can cast a veto. The candidate is hired if accepted by at least one player and not vetoed. The total number of vetoes available for each player is …xed in advance. We prove the existence of a subgame perfect equilibrium for this game if there are a …nite number of candidates types. For a general candidate distribution we prove the existence of an " subgame perfect equilibrium. We also demonstrate several unusual phenomena, including situations in which a player prefers the other player would have an extra veto, and even prefers to give his own veto right to the other player.