Core in a simple coalition formation game

We analyze the core of a class of coalition formation game in which every p layer's payoff depends only on the members of her coalition. We first consi der anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additiona l strong properties are imposed. We then introduce two top-coalition proper ties each of which guarantee the existence. We show that these properties a re independent of the Scarf-balancedness condition. Finally we give several economic applications.