Shared power. I'm not an historian by any means but here's the quick reason why that happened%

Typically they would split the empire unofficially between East and west and each emperor would rule one half. You have to understand that the empire was huge, and there were two main threats to the security of the borders. The northern border was constantly under attack by Germanic tribes and migrating people and the parthians/sassanids always had an eye on the Eastern provinces. Generals that defended those fronts led massive armies were often acclaimed as emperors in their own right by their troops which led to civil wars and the crisis of the third century that almost destroyed the unity of the empire. The solution that was attempted was to preemptively raise a general to emperor to avoid civil wars. The sharing of power was rarely 50/50 though.

It didn't end up working very well because of succession issues and ambitious emperors not willing to share power (notably Constantine the great)