Which event causes Eteocles and Polynices to engage one another in battle?

Both wanted the possession of the throne of Thebes. "When you play to game of thrones, you either kill or be killed."

The Short: After Oedipus abdicated the throne, the two brothers eventually fought in battle for the throne.

The Long: After Oedipus addicted the throne, he cursed his sons/brothers. The two boys eventually decided to take turns being king, switching places every year. But after the first year, Eteocles refused to step down and let his brother have his turn so Polynices gathered his men and they both fought in battle and ended up killing each other. A tragic fate indeed.