The paper is concerned with a nonco operative multi stage multi person game. A finite sequence of random variables is observed sequentially by k ordered players. Each player selects one variable different from those selected by others. At each stage of the game a player who has not selected a variable before is allowed to select the presented one if and only if all players with lower order numbers rejected it. Payoff functions depend on a sample and location of all selections. For game strategies of the sequential behavioral type an equilibrium solution is found by the dynamic programming method. Numerical results related to the secretary type problems are presented.