The problem of strategically supported cooperation in linear-quadratic differential games with nontranferable payoffs is considered. It is assumed, that the player uses the payoff distribution procedure to get the individual rationality of cooperative solution. To punish those who violate cooperative agreement, the special game, which differs from initial one only by the players' payoffs on cooperative trajectory is constructed. It is shown that in the new game there exists an ε-equilibrium with players' payoffs equal to corresponding cooperative players' payoffs in initial game.