  Experimental verification has been the method of choice for verifying the
stability of a multi-agent reinforcement learning (MARL) algorithm as the
number of agents grows and theoretical analysis becomes prohibitively complex.
For cooperative agents, where the ultimate goal is to optimize some global
metric, the stability is usually verified by observing the evolution of the
global performance metric over time. If the global metric improves and
eventually stabilizes, it is considered a reasonable verification of the
system's stability.
  The main contribution of this note is establishing the need for better
experimental frameworks and measures to assess the stability of large-scale
adaptive cooperative systems. We show an experimental case study where the
stability of the global performance metric can be rather deceiving, hiding an
underlying instability in the system that later leads to a significant drop in
performance. We then propose an alternative metric that relies on agents' local
policies and show, experimentally, that our proposed metric is more effective
(than the traditional global performance metric) in exposing the instability of
MARL algorithms.
