Not too far into the game, you'll encounter your first stage battle. They are, in essence, a real-time strategy concept put into the game. The goal of each stage battle (in Multiplayer, at least) is to take down the opponent's stage, while yours remains intact; single player campaign stage battles may have slightly different goals for victory. Each battle is comprised of a few components, such as the stage, fan geysers, units and a few other things.
FLYING
One of the few things that can be done in stage battles, that can't be done outside of them, is the ability for your Avatar to fly. With the click of a button, you will be able to fly around the whole battleground. This has both its advantages and disadvantages, as you can only be attacked by a few units, but you aren't able to attack at all (including solos). While flying, though, you can still give orders to units and produce new ones.
STAGE
The stage is the most important thing in a stage battle, since if yours is destroyed, then you will lose. Thus, it is imperative that you protect it at all costs. There are many ways to protect it, such as producing units and leaving them there to defend, or even Double Teaming with the stage itself to use its unique features. The stage's health is represented by 10 yellow lights, with each one representing 10% of its health.
Every stage has several defenses that one can use to help in defending it from attackers, which you do by Double Teaming with it. The first thing is the fog machine, which reduces the attack power of enemies that remain in its vicinity. You can also uses its speakers to send a blast from either side. If the stage gets damaged, you are able to heal a portion of its health back, but at the cost of 200 fans. One last defense for stages are the stage lights, which can be used by flying up to them and pressing the appropriate button; these blast breams of light at enemies, and they can be charged to fire a more destructive beam.
FAN GEYSERS
Fans are the bread and butter of stage battles, since you need them to produce new units, as well as upgrading the stage. You get more fans by capturing Fan Geysers, but may be some obstacles in your way. When you begin a stage battle, each side will always have at least one Fan Geyser to them; all of the other geysers are protected by Fan Leeches. While you can't directly attack Fan Leeches or enemy geysers with your Avatar, you can send your units to attack them instead.
After attacking an enemy geyser or a Fan Leech and the geyser is free, you can play the Fan Tribute solo to capture the fan geyser for your faction. The geyser can only be captured if the fans that are coming out of it are green; if they are red, then there are enemies nearby and they must be eliminated before the geyser can be captured.
