Repeated games: an overview of the zero-sum case

In repeated games, crucial points in the modeling deal with information: To what extent do the players know exactly what game they are playing, including the others' utilities, and to what extent are they informed of all pure strategy choices after every stage of the game? When such full information is not assumed, one is led to the so-called games with incomplete information: There are several possible games (i.e., states of nature, or types of the several players), one of which is chosen in the beginning according to some known probability distribution. Players may have some private partial information about this choice, for instance, their own type. After every stage of the game, every player gets some signal, which may depend on the state of nature, the actions of all players at this stage, and the player receiving it. I will deal mainly with the two-player zero-sum case. The zero-sum case, among others, is needed to set the limitations in the general case - such as the minimum amount an individually rational player would accept, or, more generally, the characteristic function.