Efficient evolutionary dynamics with extensive-form games

TL;DR

This paper introduces a novel replicator dynamics model for extensive-form games that significantly reduces computational complexity and is equivalent to traditional models, applicable in both discrete and continuous time.

Contribution

It presents the first replicator dynamics for the sequence form of extensive-form games, enabling exponential efficiency improvements over normal form methods.

Findings

Replicator dynamics for extensive-form games are realization equivalent to normal form dynamics.

The new dynamics are applicable in both discrete and continuous time.

Standard stability analysis tools are extended to this new framework.

Abstract

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.