Young, Stephen E. "Chapter Seven: Liturgical Tradition in the Didache: The Lord's Prayer in Did. 8.2" Jesus Tradition in the Apostolic Fathers. Tübingen: Mohr Siebeck, 2011, 201-225.
Young considers the Didache, though derived from a number of sources, to represent the redactional work of one person, whom he will call the Didachist, performed in a relatively short period of time (Young 2011, 201). Two passages are specifically ascribed to Jesus: the prayer in 8.2, and another sying in 9.5. This chapter evaluates the Lord's Prayer tradition.
As he has done in the past, Young presents the Greek text, followed by a catalog of parallel statements, this time all from the Synoptic Gospels (Young 2011, 202-203). He then observes that the text is clearly much more similar to the version in Matthew than the one in Luke. It does not have the gaps found in Luke's version, and the language is more similar to Matthew's version (Young 2011, 203).
Young analyzes C.M. Tuckett's work, "The Synoptic Tradition in the Didache" as a definitive work of analysis (Young 2011, 204ff). Tuckett concluded that the type of redactional work he could identify in the similar passages in Matthew and the Didache point to the Didachist having access to Matthew in a finished state. He also concluded that the Didachist may well have had access to Luke (Young 2011, 205). However, Tuckett onsidered parts of Didache 16 to use traditions also used by Mark or Matthew, and not to have used Mark or Matthew themselves. He finds other passages which have parallels in all the Synoptic Gospels and which he takes to be derived from a version of Matthew's revisions of Mark. The picture of literary dependence is thus quite complicated (Young 2011, 208). Young provides a lengthy footnote detailing a growing body of thought which is open to the Didache influencing Matthew rather than Matthew influencing the Didache (Young 2011, 208-209).
The crux of the challenge is well summarized in this paragraph. "If one were to determine that the Didache antedates Matthew, this would necessitate rethinking several elements of Tuckett's argument. It would imply that the so-called 'Matthean redactional features' he identifies in the Didache originated not in MattR but in the editorial work or the sources of the Didachist. The presence of these features in Matthew might then be attributed either to Matthew's dependence on the Didache, or what is more likely, to Matthew's use of sources he held in common with the Didache, whether written or oral. One would also have to rethink how to account for the features in the Didache that in Tuckett's view show MattR of Mark (an important component of his argument). These could be viewed as examples of Matthew redacting Mark under the influence either of the Didache or of sources he held in common with the Didache, in which case the apparent objectivity provided by Tuckett's appeal to material in the Didache that originated in MattR of Mark would prove illusory" (Young 2011, 209). In short, then, Young finds the question of influence to remain open, and to be one which could have significant influence on the overall study of the Synoptics and the Apostolic Fathers.
Despite the apparent close relationship of the Didache and Matthew, Young does not consider the relationship to be one of literary dependence. There are no examples of passages in which the Didache seems to quote extensively from Matthew in ways distinctive to Matthew as opposed to other Synoptists (Young 2011, 210). There are clear similarities, however, Young explains that "the Didache and Matthew sound alike because they share a common idiom and a common tradition, as documents that arose out of a shared milieu" (Young 2011, 212). Young furthernotes that the shared material may well have been part of an oral tradition. He comments that the possibility of orality is not entertained by Tuckett or some ohters (Young 2011, 214).
young observes that the Lord's Prayer is introduced in Didache 8.2 "as the Lord commanded in his gospel" (Young 2011, 218). Opinion is divided whether to consider this "gospel" as the canonical written account or as a series of sayings about sin and salvation. In any case, Young recognizes that the prayer would likely have circulated orally and, based on the description in the Didache, likely took on a liturgical function (Young 2011, 230). An oral liturgical text which was widely known and used can easily explain the identity in ideas but the variation in exact wording between the versions of the prayer in Matthew and the Didache (Young 2011, 222). The textual variants other than the concluding doxology are very slight. Young's overall conclusion is that the prayer was a matter of known liturgy and was adopted independently by Matthew and the Didachist (Young 2011, 224).