The purpose of this paper is to introduce the concept of interconnected games and to show its relevance for modeling international environmental problems. It is argued that an interconnected game approach to international environmental problems may enhance cooperation and provide an alternative to the use of financial side payments to induce countries to cooperate. Two types of interconnected games are distinguished in this paper, i.e. direct sum games and tensor games. In the former all the constituting isolated games are games in strategic form and in the latter they are repeated games. In both cases the interconnected game can be interpreted as a multiple objective game, but only the setting where a trade-off is made for the vector-payoffs is considered. In addition to the formal definition of these types of interconnected games, some elementary results concerning Nash equilibria of such games are derived.