The methods for reinforcement learning that we have seen so far relate to single agents taking decisions on an environment. We can think, however, on a slightly different kind of problem in which multiple agents jointly act on the same environment trying to maximize a common reward signal. Such environment could be robotics, networking, economics, auctions, etc. Often time, the algorithms discussed up until now would potentially fail in such environments. The problem is that in these kinds of environments, the control of the agents is decentralized and therefore it requires coordination and cooperation to maximize the reward signal.
Even though decentralizing the decision-making adds considerable complexity, the need for a multi-agent system for some problems is real. Often a centralized approach is just not possible, perhaps due to physical constraints, for example, a network routing system being decentralized, or a team of robots with shared objectives but independent processing capabilities. So, the methods of decentralized reinforcement learning, often called Dec-MDPs and Dec-POMDPs, are very important as well.
When other agents take actions on the same environment, game theory becomes important. Game theory is a field that researches conflict of interests. Economics, political science, psychology, biology and so on are some of the most conventional fields using game theory concepts.