  The field of multi-agent reinforcement learning (MARL) has made considerable
progress towards controlling challenging multi-agent systems by employing
various learning methods. Numerous of these approaches focus on empirical and
algorithmic aspects of the MARL problems and lack a rigorous theoretical
foundation. Graphon mean field games (GMFGs) on the other hand provide a
scalable and mathematically well-founded approach to learning problems that
involve a large number of connected agents. In standard GMFGs, the connections
between agents are undirected, unweighted and invariant over time. Our paper
introduces colored digraphon mean field games (CDMFGs) which allow for weighted
and directed links between agents that are also adaptive over time. Thus,
CDMFGs are able to model more complex connections than standard GMFGs. Besides
a rigorous theoretical analysis including both existence and convergence
guarantees, we provide a learning scheme and illustrate our findings with an
epidemics model and a model of the systemic risk in financial markets.
