The dynamic linear – quadratic two player’ game problem with vector m1 (m2)-component payoff for the first (the second) player is studied. As a problem’s decision the cone equilibrium is considered. As a rule, there are a lot of such situations. In article an equilibrium situation refinement on the expert estimation basis is offered. The dynamic game problem with vector payoffs is reduced to a noncooperative differential two person’ game. The equilibrium decision in last problem is studied under recipes of the Bellman’s dynamic programming. The modeling example is presented.