The solution formula for the payoff distribution procedure of a bargaining problem in a cooperative differential game with nontransferable payoffs that lead to a time consistent outcome is proposed by Leon A. Petrosyan and D. W. K. Yeung (2014). In this paper we study this formula for linear-quadratic discrete-time dynamic games with nontransferable payoffs. Pareto-optimal solution is studied as optimality principle. The time consistency and irrational behavior proof condition of this solution are investigated. As an example the government debt stabilization game is considered.