Well-Posedness of Weakly Cooperative Equilibria for Multi-objective Population Games

In this paper, we construct a bounded rationality function of weakly cooperative equilibrium point of multi-objective population games (WCEPOMPG) by virtue of nonlinear scalarization function. We investigate lower semicontinuity of the bounded rationality function and present a relationship between the level set of zero of the bounded rationality function and WCEPOMPG. By applying these properties, we first consider the generalized well-posedness for WCEPOMPG in the setting of multiple-valued assumption of solution set. Then, we obtain the uniqueness of solution set on a dense residual set with the stable assumption of vector payoff functions. Moreover, we investigate the well-posedness of WCEPOMPG on the dense residual set. As a special case, we obtain the generalized well-posedness and well-posedness of cooperative equilibria for single-objective population games, respectively.