The Smart Grid is defined as a large-scale electrical grid that can amalgamate the actions of whole users connected to it — generators, consumers and those that do both. Now, the technologies should lie on the abstract mathematics firmly to model and control the operations. Game theory is a mathematical tool to model systems with multi-agents (rational decision-makers). Game theory models the behavior of independent and rational agents which they want to maximize their profits. To this end, we model the behavior of agents and the possible behaviors profit. In the new system, users are able to generate the required energy from renewable energy sources such as solar panels, electric generators, and so forth. Hence, in these complex systems, we would make the use of the mathematical tools to model the interactions and features between the entities. In this paper, three basic questions will be answered which I) Why cooperation between agents is valuable. II) Which forms of cooperation are forming and III) Why and how game theory can model the cooperation. In the following, we survey a number of Game theory-based applications especially cooperative game theory to solve relevant problems in Smart Grid. Smart grid mainly is divided into three branches including Distributed electricity generation (Micro-grid), Demand Side Management (DSM), and Communications that we will describe the applications of game theory in Micro-grid in detail in the following.