On the alpha-core of set payoffs games

This paper deals with a-core of set payoffs games with finitely many players and finite coalition alpha-core of set payoffs games with infinitely many players. We present an existence theorem of alpha-core of set payoffs games with finitely many players. By virtue of finite intersection property, we also establish an existence theorem of finite coalition alpha-core of set payoffs games with infinitely many players. Besides, we obtain some stability results of solution mapping of a-core of set payoffs games, where set payoff functions and action sets of agents involve perturbed parameters. Moreover, as applications, we obtain the corresponding results for alpha-core of vector payoffs games.