Stability of the core mapping in games with a countable set of players

Greenberg (1990) and Ray (1989) showed that in coalitional games with a finite set of players the core consists of those and only those payoffs that cannot be dominated using payoffs in the core of a subgame. We extend the definition of the dominance relation to coalitional games with an infinite set of players and show that this result may not hold in games with a countable set of players (even in convex games). But if a coalitional game with a countable set of players satisfies a mild continuity property, its core consists of those and only those payoff vectors which cannot be dominated using payoffs in the core of a subgame.