  Though limited in real-world decision making, most multi-agent reinforcement
learning (MARL) models assume perfectly rational agents -- a property hardly
met due to individual's cognitive limitation and/or the tractability of the
decision problem. In this paper, we introduce generalized recursive reasoning
(GR2) as a novel framework to model agents with different \emph{hierarchical}
levels of rationality; our framework enables agents to exhibit varying levels
of "thinking" ability thereby allowing higher-level agents to best respond to
various less sophisticated learners. We contribute both theoretically and
empirically. On the theory side, we devise the hierarchical framework of GR2
through probabilistic graphical models and prove the existence of a perfect
Bayesian equilibrium. Within the GR2, we propose a practical actor-critic
solver, and demonstrate its convergent property to a stationary point in
two-player games through Lyapunov analysis. On the empirical side, we validate
our findings on a variety of MARL benchmarks. Precisely, we first illustrate
the hierarchical thinking process on the Keynes Beauty Contest, and then
demonstrate significant improvements compared to state-of-the-art opponent
modeling baselines on the normal-form games and the cooperative navigation
benchmark.
