I’ve had a hard time getting to the root of the issue here. Was this Shakespeare or not Shakespeare? Did he collaborate? And how sure are we that he did? I’ll come back to this question as I march through the play, but I want to hear from the blogosphere about the issue. Who has the lowdown here?
I ask because as I read, the play is impressing me by the page. It’s not that it’s the most compelling play I’ve ever written, but it seems remarkably thoughtful and consistent to itself, and resonates with many familiar moments and metaphors from other plays and the sonnets. The only site with the most information I could find on the short term was the wikipedia page, and so I reprint what they have here for you on this issue:
In 1596, Edward III was published anonymously (although this was not uncommon in the 1590s). The principal arguments against Shakespeare’s authorship include the facts that John Heminges and Henry Condell did not include the play when they compiled the First Folio of Shakespeare’s plays in 1623, nor is it mentioned in Francis Meres‘ Palladis Tamia (1598), a work that lists many (but not all) of Shakespeare’s early plays. Also, some critics view the play as not worthy of Shakespeare’s writing ability. Despite this, many critics have seen some passages as having a Shakespearean ring to them. In 1760, noted Shakespearean editor Edward Capellincluded the play in his Prolusions; or, Select Pieces of Ancient Poetry, Compil’d with great Care from their several Originals, and Offer’d to the Publicke as Specimens of the Integrity that should be Found in the Editions of worthy Authors, and concluded that it had been written by Shakespeare. However, Capell’s conclusion was not embraced by scholars.
In recent years, professional Shakespeare scholars have increasingly reviewed the work with a new eye, and have concluded that some passages are as sophisticated as any of Shakespeare’s early histories, especially King John and the Henry VI plays. In addition, passages in the play are direct quotes from Shakespeare’s sonnets. Stylistic analysis has also produced evidence that at least some scenes were written by Shakespeare. In the Textual Companion to the Oxford Complete Works of Shakespeare, Gary Taylor states that “of all the non-canonical plays, [Edward III] has the strongest claim to inclusion in the Complete Works” (the play was subsequently edited by William Montgomery and included in the second edition of the Oxford Complete Works, 2005). The first major publishing house to produce an edition of the play was Cambridge University Press as part of its New Cambridge Shakespeare series. Since then, an edition of the Riverside Shakespeare has included the play, and plans are afoot for the Arden Shakespeare and Oxford Shakespeareseries to publish editions. Giorgio Melchiori, editor of the New Cambridge edition, asserts that the play’s disappearance from the canon is probably due to a 1598 protest at the play’s portrayal of the Scottish. According to Melchiori, scholars have often assumed that this play, the title of which was not stated in the letter of 15 April 1598 from George Nicolson(Elizabeth I‘s Edinburgh agent) to Lord Burghley noting the public unrest, was a comedy (one that does not survive), but the play’s portrayal of Scots is so virulent that it is likely that the play was, officially or unofficially, banned, and left forgotten by Heminges and Condell. (Melchiori, 12–13)
Some scholars, notably Eric Sams, have argued that the play is entirely by Shakespeare, but today, scholarly opinion is divided, with many researchers asserting that the play is an early collaborative work, of which Shakespeare wrote only a few scenes.
In 2009, Brian Vickers published the results of a computer analysis, with a program designed to detect plagiarism, which suggest that 40% of the play was written by Shakespeare with the other scenes written by Thomas Kyd (1558–1594).
- George Peele — Tucker Brooke (1908)
- Christopher Marlowe, with Robert Greene, George Peele, and Thomas Kyd — J.M. Robertson (1924)
- Michael Drayton— E.A. Gerard (1928) and H.W. Crundell (1939)
- Robert Wilson — S.R. Golding (1929)
- William Shakespeare — A.S. Cairncross (1935)
- Thomas Kyd — W. Wells (1940) and G. Lambrechts (1963)
- Robert Greene — R.G. Howarth (1964)
- William Shakespeare — Elliott Slater (1988), Eric Sams (1996)
- William Shakespeare and one other — Jonathan Hope (1994)
- William Shakespeare and Christopher Marlowe — Robert A.J. Matthews and Thomas V.N. Merriam (1994)
- William Shakespeare and others (not Marlowe) — Giorgio Melchiori (1998) 
- Thomas Kyd (60%) and William Shakespeare (40%) — Brian Vickers (2009)