  Several multiagent reinforcement learning (MARL) algorithms have been
proposed to optimize agents decisions. Due to the complexity of the problem,
the majority of the previously developed MARL algorithms assumed agents either
had some knowledge of the underlying game (such as Nash equilibria) and/or
observed other agents actions and the rewards they received.
  We introduce a new MARL algorithm called the Weighted Policy Learner (WPL),
which allows agents to reach a Nash Equilibrium (NE) in benchmark
2-player-2-action games with minimum knowledge. Using WPL, the only feedback an
agent needs is its own local reward (the agent does not observe other agents
actions or rewards). Furthermore, WPL does not assume that agents know the
underlying game or the corresponding Nash Equilibrium a priori. We
experimentally show that our algorithm converges in benchmark
two-player-two-action games. We also show that our algorithm converges in the
challenging Shapleys game where previous MARL algorithms failed to converge
without knowing the underlying game or the NE. Furthermore, we show that WPL
outperforms the state-of-the-art algorithms in a more realistic setting of 100
agents interacting and learning concurrently.
  An important aspect of understanding the behavior of a MARL algorithm is
analyzing the dynamics of the algorithm: how the policies of multiple learning
agents evolve over time as agents interact with one another. Such an analysis
not only verifies whether agents using a given MARL algorithm will eventually
converge, but also reveals the behavior of the MARL algorithm prior to
convergence. We analyze our algorithm in two-player-two-action games and show
that symbolically proving WPLs convergence is difficult, because of the
non-linear nature of WPLs dynamics, unlike previous MARL algorithms that had
either linear or piece-wise-linear dynamics. Instead, we numerically solve WPLs
dynamics differential equations and compare the solution to the dynamics of
previous MARL algorithms.
