Did William Shakespeare really exist?

Although Elizabethan playwright Christopher Marlowe is to now be credited by Oxford University Press as Shakespeare's co-writer on three of the Bard's plays, the two playwrights, allegedly born two weeks apart, perhaps poses the antithesis of Marlovian theory. However, the strange circumstances around the death of Marlowe and his expiry at the hands of murder due to debts owed, in conjunction with Shakespeare’s first publication, Venus and Adonis appearing only weeks after Marlowe’s death is food for thought. Marlowe, here had cause to fake his own death which is aptly supported by ambiguities regarding the event of his death and fragmentary witness reports. This, in close connection with Marlowe's association with Shakespeare’s plays as a co-contributor as well as the lack of documentation relating to Shakespeare’s actual birth in Stratford Upon Avon, gives birth to the question as to whether William Shakespeare existed at all and whether or not the famous bard as we know him, was perhaps merely a fictitious pseudonym.