Аннотация:

This paper studies the problem of whether an $\alpha$-core exists (is non-empty) for generalized normal-form games where player payoffs are described by point-to-set convex-valued, irreflexive, and weakly continuous preferences. We propose a short effective proof of the non-emptiness of the core; it based on a contradiction with Brouwer's theorem on the existence of a fixed point for a continuous mapping of a convex compact set into itself.