Further Developments of Extensive-Form Replicator Dynamics using the Sequence-Form Representation

Replicator dynamics model the interactions and change in large populations of agents. Standard replicator dynamics, however, only allow single action interactions between agents. Complex interactions, as modeled by general extensive games, have received comparatively little attention in this setting. Recently, replicator dynamics have been adapted to extensive-form games represented in sequence form, leading to a large reduction in computational resource requirements. In this paper, we first show that sequenceform constraints and realization equivalence to standard replicator dynamics are maintained in general n-player games. We show that sequence-form replicator dynamics can minimize regret, leading to equilibrium convergence guarantees in two-player zero-sum games. We provide the first empirical evaluation of sequence-form replicator dynamics, applied to n-player Kuhn poker with two, three, and four players. Our results show that the average strategies generated by sequence-form replicator dynamics produce approximate equilibrium strategies with increasing accuracy over time.