A growing awareness of the prominent role the environment plays in multi-agent systems has led to gradual acceptance of its importance by the multi-agent system community in general. Within this line of research, we propose a new class of games, called Multi-Games. A Multi-game is one in which a given number of players play a fixed finite number of basic games simultaneously. The basic games in a multi-game can be regarded as different environments for the players, and, in particular, we submit that multi-games can be used to model investment in multiple national and continental markets within a global economy. Furthermore, when the players' weights for different games in the multi-game are classed as private information or as types with given conditional probability distributions, we obtain a particular class of Bayesian games. The main contribution of this thesis is to illustrate how, for the class of so-called completely pure regular multi-games with finite sets of types, the Nash equilibria of the basic games can be used to compute a Bayesian Nash equilibrium in multi-games, with complexity independent of the number of types. Following the presentation of the main results, the thesis presents two algorithms that allow us to establish whether we have a Bayesian Nash equilibrium which can be determined with lower computational complexity.