Sequence-Form and Evolutionary Dynamics: Realization Equivalence to Agent Form and Logit Dynamics

Evolutionary game theory provides the principal tools to model the dynamics of multi–agent learning algorithms. While there is a long–standing literature on evolutionary game theory in strategic–form games, in the case of extensive–form games few results are known and the exponential size of the representations currently adopted makes the evolutionary analysis of such games unaffordable. In this paper, we focus on dynamics for the sequence form of extensive–form games, providing three dynamics: one realization equivalent to the normal–form logit dynamic, one realization equivalent to the agent–form replicator dynamic, and one realization equivalent to the agent–form logit dynamic. All the considered dynamics require polynomial time and space, providing an exponential compression w.r.t. the dynamics currently known and providing thus tools that can be effectively employed in practice. Moreover, we use our tools to compare the agent–form and normal– form dynamics and to provide new "hybrid" dynamics.