Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems

Yuzuru Sato
Brain Science Institute
The Institute of Physical and Chemical Research (RIKEN)
2-1 Hirosawa, Saitama 351-0198, Japan
and
Santa Fe Institute
1399 Hyde Park Rd.
Santa Fe, NM 87501, USA
James P. Crutchfield
Santa Fe Institute
1399 Hyde Park Rd.
Santa Fe, NM 87501, USA

ABSTRACT: Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through the environment. As an application, with a rock-scissors-paper game interaction between agents, the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos---behaviors that are to be expected in the multiagent, heterogeneous setting described by the general replicator equations.


Y. Sato and J. P. Crutchfield, "Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems", Physical Review E 67:1 (2003) 40-43. [ps.gz]= 1,561kb [ps]= 5,664kb [pdf]3,279kb.
Santa Fe Institute Working Paper 02-04-017. http://arXiv.org/abs/nlin/0204057.