Abstract We consider a bilateral secretary problem of which model is as follows: n objects appear sequentially and completely randomly for the players I, II. The player I has the first option to stop and accept this object or to reject it, if and only if the player I rejects it then the player II has the same option. Knowledge about the current object (jth) is restricted to its relative rank among the first j objects which has already appeared and both players the same knowledge at any point. We call “win” for the player to stop and accept the best object (absolute rank 1 of all) or the second best object (absolute rank 2 of all). If this event “win” attains by some player, he gain a payoff of which structure is defined in section 1. When one player stops, the other player cannot stop and only observes. This game is formulated by zero sum game without recall. We derive the optimal stopping policies for both players and the value of the game. Moreover we study the asymptotic case.