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.