  Independent learners are agents that employ single-agent algorithms in
multi-agent systems, intentionally ignoring the effect of other strategic
agents. This paper studies mean-field games from a decentralized learning
perspective, with two primary objectives: (i) to identify structure that can
guide algorithm design, and (ii) to understand the emergent behaviour in
systems of independent learners. We study a new model of partially observed
mean-field games with finitely many players, local action observability, and a
general observation channel for partial observations of the global state.
Specific observation channels considered include (a) global observability, (b)
local and mean-field observability, (c) local and compressed mean-field
observability, and (d) only local observability. We establish conditions under
which the control problem of a given agent is equivalent to a fully observed
MDP, as well as conditions under which the control problem is equivalent only
to a POMDP. Building on the connection to MDPs, we prove the existence of
perfect equilibrium among memoryless stationary policies under mean-field
observability. Leveraging the connection to POMDPs, we prove convergence of
learning iterates obtained by independent learning agents under any of the
aforementioned observation channels. We interpret the limiting values as
subjective value functions, which an agent believes to be relevant to its
control problem. These subjective value functions are then used to propose
subjective Q-equilibrium, a new solution concept for partially observed
n-player mean-field games, whose existence is proved under mean-field or global
observability.We provide a decentralized learning algorithm for partially
observed n-player mean-field games, and we show that it drives play to
subjective Q-equilibrium by adapting the recently developed theory of
satisficing paths to allow for subjectivity.
