The n-person differential game Γ(x₀,T-t₀) with prescribed duration and independent motions is considered. The regularization of the game is constructed which alters players payoffs along the so-called 'optimal trajectory' maximizing the sum of players payoffs. It is shown that in a regularized game Γ_α(x₀,T-t₀) there always exist the Nash equilibria with cooperative payoffs. Under some additional assumptions it is proved that these equilibria are strong, i.e. stable against deviations of coalitions.