Suppose that players I and II want to jointly employ two secretaries successively one-by-one from a set of $n$ applicants. Best ability of management (foreign language) is wanted by I (II). We assume that these two kinds of abilities are mutually independent for every applicant. Applicants present themselves one-by-one sequentially. Facing each applicant, each player chooses either to Accept or to Reject. The game ends either when the second time of choice-pair A--A happens getting the payoffs predetermined by the game rule, or when $n-2$ applicants except the last two are rejected. If choice-pair is A--R or R--A, then arbitration comes in and forces players to take the same choice as I's (II's) with probability $p\ (\bar{p}), \frac12\leq p\leq 1$. Each player aims to maximize the expected payoff he can get. Explicit solutions are derived to this $n$-stage game, for the cases where abilities of each applicant are observed as bivariate random variables with full-information and with no-information. Some numerical results are presented.