The research group supported by the Momentum Programme of the Hungarian Academy of Sciences aims at understanding, modelling and solving certain problems within the realm of game theory. The focus of research is at cooperative games, where the players’ interactions generate externalities, that is, third parties, not directly participating in the activities may get affected. In partition function form games the third party is a third player or another coalition, while in dynamic cooperative games it may well be the future self of one of the acting agents. While noncoperative game theory is based on the Nash equilibrium and its variants, one of the beauties of cooperative game theory is precisely the multiplicity of solutions, that the same question can be answered in multiple ways. The problems studied are not entirely new, one of the goals is to explore the relation of the existing answers, combine their advantages, while also developing entirely new approaches. Besides the theoretical results the aim is also to apply them in economic models. The natural areas where cooperative games with externalities can be applied include the voluntary provision of public goods, the stability of international environmental agreements, the collaboration of market players, that is, cartels, free trade areas or research cooperations. The applications of power indices and matching models are especially prominent in the research profile.