In this paper, we establish the bounded rationality model M for generalized vector equilibrium problems by using a nonlinear scalarization technique. By using the model M, we introduce a new well-posedness concept for generalized vector equilibrium problems, which unifies its Hadamard and Levitin-Polyak well-posedness. Furthermore, sufficient conditions for the well-posedness for generalized vector equilibrium problems are given. As an application, sufficient conditions on the well-posedness for generalized equilibrium problems are obtained. MSC: 49K40; 90C31

Under the assumption that the range of varying uncertain parameters is known, some results of existence and stability of equilibria for population games with uncertain parameters are investigated in this paper. On the basis of NS equilibria in classical noncooperative games, the concept of NS equilibria for population games with uncertain parameters is defined. Using some hypotheses about the continuity and convexity of payoff functions, the existence of NS equilibria in population games is also proved by Fan–Glicksberg fixed point theorem. Furthermore, we establish a bounded rationality model of population games with uncertain parameters, and draw the conclusions about the stability of NS equilibrium in this model by constructing the rationality function and studying its properties.

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In this paper, we first construct a complete metric space Λ consisting of a class of strong vector equilibrium problems (for short, (SVEP)) satisfying some conditions. Under the abstract framework, we introduce a notion of well-posedness for the (SVEP), which unifies its Hadamard and Tikhonov well-posedness. Furthermore, we prove that there exists a dense G δ set Q of Λ such that each (SVEP) in Q is well-posed, that is, the majority (in Baire category sense) of (SVEP) in Λ is well-posed. Finally, metric characterizations on the well-posedness for the (SVEP) are given.