Coordinating partially-informed agents over state-dependent networks

We consider a multi-agent scenario with K ≥ 2 agents that have partial information about some random nature state, and that take actions in a repeated manner. Each agent also has imperfect observations of the other agents' past actions and the nature state realization. Our goal is to characterize the set of asymptotically implementable distributions on the agents' actions and the nature state. We solve this problem for general K when all agents have only causal nature state information (NSI) and for K = 2 when: one agent has causal NSI and the other agent has non-causal NSI; or in some special cases when both agents have non-causal NSI.