Motivated by recent path-breaking contributions in the theory of repeated games

in continuous time, this paper presents a family of discrete-time games which provides

a consistent discrete-time approximation of the continuous-time limit game.

Using probabilistic arguments, we prove that continuous-time games can be defined

as the limit of a sequence of discrete-time games. Our convergence analysis reveals

various intricacies of continuous-time games. First, we demonstrate the importance

of correlated strategies in continuous-time. Second, we attach a precise meaning to

the statement that a sequence of discrete-time games can be used to approximate a

continuous-time game.