Chapter 2. Advances in Zero-Sum Dynamic Games

The survey presents recent results in the theory of two-person zero-sum repeated games and their connections with differential and continuous-time games. The emphasis is made on the following (1) A general model allows to deal simultaneously with stochastic and informational aspects. (2) All evaluations of the stage payoffs can be covered in the same framework (and not only the usual Cesàro and Abel means). (3) The model in discrete time can be seen and analyzed as a discretization of a continuous time game. Moreover, tools and ideas from repeated games are very fruitful for continuous time games and vice versa. (4) Numerous important conjectures have been answered (some in the negative). (5) New tools and original models have been proposed. As a consequence, the field (discrete versus continuous time, stochastic versus incomplete information models) has a much more unified structure, and research is extremely active.