© 2015 IEEE. The problem of strategically supported cooperation in linear-quadratic differential games is considered. It is assumed, that the cooperative agreement is reached and each player gets his payoff according to the payoff distribution procedure [5]. Following [3], to punish those who violate this agreement, the special game, which differs from initial only by payoffs of players on cooperative trajectory is constructed. It is shown that in the new game there exists an ε-equilibrium with payoffs of players equal to corresponding payoffs of players in cooperative solution of initial game.