re in Games with Externalities

In the presence of externalities across coalitions, Dutta et al. (2010) characterize their value by extending Hart and Mas-Colell reduced game consistency. In the present paper, we provide a characterization result for the core for games with externalities by extending one form of consistency studied by Moulin (1985), which is often refereed to as the complement-reduced game property. Moreover, we analyze another consistency formulated by Davis and Maschler (1965), called the max-reduced game property and a final consistency called the projection-reduced game property. In environments with externalities, we discuss some asymmetric results among these different forms of reduced games.