In this talk I will give an overview on recent topics in continuous-time game theory. The first part of the talk will be concerned with the question of whether continuous-time game theory can be understood as the formal limit of a sequence of discrete-time games. Using weak convergence arguments and martingale techniques some positive and some negative results will be derived. From a conceptual point of view this limit analysis clearly shows in what sense continuous-time game theory can be interpreted from the point of view of sequential interactive decision theory, and what special features continuous-time games have. The second part of the talk uses the tractability of the continuous-time model to derive some new geometric characterizations of the set of perfect public equilibrium payoffs in a class of games where players have a Brownian information structure.
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