With the popularization of Electric Vehicles (EVs) and the continuous upgrading of Vehicle to Grid (V2G) discharging technology, electric vehicles, as a kind of high-quality energy storage resource, play an important role in the balance regulation of power system. Due to the limited contribution of charging and discharging power for single EV, EVs participate balance market generally by virtual power plants or EV aggregators. This paper proposed a three-round bidding mechanism for balance market based on game theory. Stackelberg model was implemented to simulate the interaction between system operator (SO) and aggregators, and incomplete information game was introduced to simulate the competition between different types of aggregators. A numerical case with four trading periods and five types of aggregators was implemented, while the bidding results of different types of aggregators participating in each period were analyzed. The effectiveness and practicability of the proposed scheme and strategy was proved by case study.