He is completely selfish.
Enkidu learns of Gilgamesh's intent to go to a wedding and impose his will on the bride before her husband can sleep with her, and is appalled, and determines to fight him, blocking his way. As a traveler explains it to Enkidu, He will have intercourse with the 'destined wife,' he first, the husband afterward. (Tablet II, lines 51 - 52). Enkidu determines to stop him. While this encounter leads to a fight, it also demonstrates that kings can be wrong, that citizens can stand up to despotic rulers, and that eventually, good rulers do their country a service by considering the opinions of others.
Because the gods create a worthy companion for him in the form of Enkidu, Gilgamesh learns to open his heart and mind not only to other people but other perceptions as well, thus turning him into a ruler who can no longer think only of himself but someone who must consider the welfare of his country as well. However, it is an epic struggle for Gilgamesh to get to this point. Even his quest is a selfish quest to find immortality for himself. However, Enkidu balances Gilgamesh. The two of them together are better than either of them by themselves, demonstrating that even absolute rulers should have wise advisers.
We see the value of a ruler who accepts the advice and wisdom again in Tablet V. Enkidu, who was born in the wild and only civilized after he established a relationship with a prostitute who taught him how to act as a human, is familiar with the wild countryside they are exploring. As they enter the Forest of Cedars, Enkidu tells Gilgamesh that he is familiar with the area and can act as his guide. In addition, Enkidu is familiar with Humbaba, the being they intend to pursue and conquer. Gilgamesh accepts his help and demonstrates the value of advisors in a good government.
In Tablet VI we see again a demonstration that a good ruler does not try to govern entirely by himself when the goddess Ishtar releases the "Bull of Heaven" on the countryside.
