Problem: Genesis presents this battle as factually true. But, according to the Documentary Hypothesis of biblical criticism, this story is a later addition and totally fictitious.
Solution: We possess very little information about this period apart from Genesis itself. As a result, while we do not have direct archaeological confirmation, there is no good reason to doubt the event. Such doubt usually stems from an anti-biblical bias.
Furthermore, there is indirect support for the validity of this account. Noted archaeologist W.F. Albright has observed that, “In spite of our failure hitherto to fix the historical horizon of chapter 14, we may be certain that its contents are very ancient. There are several words and expressions found nowhere else in the Bible and are now known to belong to the second millennium [b.c.]. The names of the towns in Transjordania are also known to be very ancient” (Alleman and Flack, Old Testament Commentary, Philadelphia: Fortress Press, 1954, 14). In light of this, there is no good reason to doubt the authenticity of the biblical account of Abraham’s battle with these Mesopotamian kings.