Motivated by the concept of cooperative equilibria with a single objective, we introduce the concepts of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. We give some examples to explain the difference between the cooperative equilibrium point and noncooperative equilibrium point of multi-objective population games. Under appropriate assumptions, we study the existence and stability of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games.

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games.

A new existence result of -vector equilibrium problem is first obtained. Then, by using the existence theorem of -vector equilibrium problem, a weakly -cone saddle point theorem is also obtained for vector-valued mappings.