| 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.