Finite-stage repeated n-person prisoner's dilemma is considered. The paper presents the new strategy profile with high payoffs for the players and stable in some sense against coalitional or individual deviations. It is proved that there exists an equilibrium profile with maximal joint payoff of players during the first steps. On the next stages the profile of strategies stable against individual deviations. This study explores the number of steps k* and the possibility of effective punishment, which provides effective cooperation such that the deviation of all possible coalitions results strictly reduced common utility.