Any biography of Shakespeare has to be based on supposition. As Rodney Bolt demonstrates (quoting Mark Twain), the facts of the playwright’s life can be set out in about four pages. The most recent significant biography of Shakespeare, Stephen Greenblatt’s “Will in the World” was a work of prodigious scholarship, but what made it appealing was its daring speculations.

Mr. Greenblatt extrapolated the meager data well beyond what a biography can sustain. His suggestion that Shakespeare may have been a closet Catholic, for example, is fascinating but inconclusive. What made Mr. Greenblatt so readable was that he made the project of outing Shakespeare so urgent and intense.

We want to solve the mystery of Shakespeare, that Mona Lisa of writers. Shakespeare’s plays, from the biographer’s point of view, are an affront, the ruses of the writer of writers, the master of disguise, whose greatness resides in his resistance to biographical inquiry even as he exposes humanity’s secrets. “Shakespeare said,” we quote as if to recognize certain truths that he first fixed in words.

So what if Shakespeare was, in fact, an alias?

What if, Mr. Bolt asks in “History Play” (Bloomsbury USA, 400 pages, $24.95), “Shakespeare” was, in truth, the pseudonym of Christopher Marlowe? Marlowe, thought to have been murdered in a tavern while brawling, might really have been a secret agent ensconced in an underground existence that allowed him to create drama unfettered by the rude and rough affairs of Elizabethan England that had threatened to suffocate his genius.

Mr. Bolt is not serious. He means to have fun with the genre and scrupulously documents the facts he proceeds to play with. He is a good sport who believes in observing the rules. He does not doubt the facts of history, but rather the fanciful way biographers bully them to tell their stories. In short, “History Play” should be required reading for biographers and consumers of biography.

Yet “History Play” is a disturbing book for biographers, because Mr. Bolt mocks one of biography’s favorite maneuvers: finding the subject’s life in his work. Mr. Bolt repeatedly discovers evidence of Marlowe’s life in Shakespeare’s writing, so dazzling the reader that at times it begins to seem as if, in deed, Marlowe and Shakespeare are interchangeable.

And if that is so, then either Shakespeare was Marlowe, or biography is such an elastic form that Mr. Greenblatt’s own speculation (amounting to novelization) is only an extreme form of the norm. Biography is a bastard form of literature; lacking a lineage, the biographer becomes a pretender.

Of course, such an alarming conclusion depends on the examples chosen. No one can convince me that, say, T.S. Eliot and Ezra Pound were the same person. Too much is known about these two characters to entertain such a conceit. All the same, there is much that biographers cannot know even about lives that have been archived and recorded. And while finding the life in the work is irresistible to biographers, this strategy can seem a dodge, a desperate effort to recover what has been lost or deliberately destroyed.

This is why Mr. Bolt proposes “The Impossibility of Biography” as an alternative title for his book.

“History Play” is pseudoscholarly fun; Mark Anderson’s “Shakespeare by Another Name” (Gotham, 640 pages, $32.50), on the other hand, is in dead earnest. The source notes alone take up nearly 200 pages. Mr. Anderson’s book resurrects the old saw that Shakespeare, a poor, ill-educated player, could not possibly have been the author of the world’s greatest plays, concluding that scholars have perpetuated an extraordinary legend.

Mr. Anderson’s candidate has always been one of those in the running – as the biographer acknowledges – but 10 years of “exhaustive research” have confirmed for Mr. Anderson that Edward de Vere, the Earl of Oxford, was in fact Shakespeare, and that in order to thrive as Shakespeare, he paid the price of making sure his true identity would never be discovered.

Well, here we have a problem, since Mr. Anderson purports to have outed the earl.

Other than selecting different candidates, there is a symmetry to books like Mr. Bolt’s and Mr. Anderson’s. They both arise out of frustration with the feeble factual record. Both play up coincidences between Marlowe and Shakespeare and Shakespeare and Oxford. After reading Mr. Bolt, though, and finding so much of Marlowe in Shakespeare, how can I take Mr. Anderson seriously?

If Mr. Anderson is less satisfying than either Mr. Bolt or Mr. Greenblatt, it is because he believes his work to be the most conclusive. How could Will Shakespeare, the player, possibly have written such great plays, and then not left any record of what he thought of them – or even made a will or left other documents to show that he valued his work? There is no scrap of paper with Shakespeare’s writing on it, Mr. Anderson notes. But where, I ask, is the Shakespeare manuscript written in the earl’s hand?

Tantalizing parallels between the plays and Oxford’s life certainly exist – but, then, I find parallels between my own life and the plays. Could I be Shakespeare?

Like all manic conspiracy theorists, Mr. Anderson has a knack for finding fishy aspects of the traditional view that Shakespeare was Shakespeare. We do not even know if Shakespeare received any education, although most scholars (but not Mr. Anderson) think the playwright attended at least grammar school. If so, Shakespeare stands with the likes of William Faulkner and other writers who had little, if any, formal schooling.

If I still lean toward Mr. Greenblatt, it is because he portrays a Shakespeare who did not want to be known as a person or as a playwright. What we know of him is mainly from legal records no man could avoid generating. It is as if Shakespeare were putting into practice T.S. Eliot’s theory of impersonality, that the author’s personality becomes subsumed – annihilated actually – by the production of a great work of art.

But here I am speculating, just as these biographers do. Alfred Lord Tennyson said he was grateful that almost nothing was known about Shakespeare, so that his work could be better appreciated. I understand the sentiment but reject it, as all incorrigible biographers do.

And not just biographers. Think what a sensation it would be to discover one of Shakespeare’s letters (assuming he did write letters). Who would say, “No, I’m not going to read it. It will spoil my enjoyment of the plays.” So other biographers will write books like the three discussed here. In “Shakespeare,” Matthew Arnold explains why:

Others abide our question. Thou art free,
We ask and ask – Thou smilest and art still,
Out-topping knowledge.