  Evolutionary game theory combines game theory and dynamical systems and is
customarily adopted to describe evolutionary dynamics in multi-agent systems.
In particular, it has been proven to be a successful tool to describe
multi-agent learning dynamics. To the best of our knowledge, we provide in this
paper the first replicator dynamics applicable to the sequence form of an
extensive-form game, allowing an exponential reduction of time and space w.r.t.
the currently adopted replicator dynamics for normal form. Furthermore, our
replicator dynamics is realization equivalent to the standard replicator
dynamics for normal form. We prove our results for both discrete-time and
continuous-time cases. Finally, we extend standard tools to study the stability
of a strategy profile to our replicator dynamics.

Computer Science and Game Theory