  This paper considers multi-agent reinforcement learning (MARL) where the
rewards are received after delays and the delay time varies across agents and
across time steps. Based on the V-learning framework, this paper proposes MARL
algorithms that efficiently deal with reward delays. When the delays are
finite, our algorithm reaches a coarse correlated equilibrium (CCE) with rate
$\tilde{\mathcal{O}}(\frac{H^3\sqrt{S\mathcal{T}_K}}{K}+\frac{H^3\sqrt{SA}}{\sqrt{K}})$
where $K$ is the number of episodes, $H$ is the planning horizon, $S$ is the
size of the state space, $A$ is the size of the largest action space, and
$\mathcal{T}_K$ is the measure of total delay formally defined in the paper.
Moreover, our algorithm is extended to cases with infinite delays through a
reward skipping scheme. It achieves convergence rate similar to the finite
delay case.
