IN 1966, BOB DYLAN visited Andy Warhol’s Factory studio in Midtown Manhattan and sat — saturnine, gnostic, impossibly young — for a Screen Test, one of the short film portraits Warhol started making in 1964 of a number of celebrities, including Dennis Hopper and Edie Sedgwick. Star-struck by his subject, Warhol offered Dylan a painting: a 1963 silk-screened portrait of Elvis Presley, of whom Dylan once said, “Hearing him for the first time was like busting out of jail.” (The portrait, ironically, is taken from a publicity still of Elvis from the Western film “Flaming Star,” in which he looks very sheriff-like.) Dylan accepted the painting — but was then faced with the problem of maneuvering the nearly seven-foot-long canvas into his station wagon. Finally, he tied it to the roof with the help of his friend, the filmmaker Barbara Rubin. Later, when the artist asked Dylan about the painting, the musician admitted that he’d given it to his manager. “But if you gave me another one, Andy, I wouldn’t make that mistake again,” Dylan reportedly said. Only later did Warhol find out that Dylan had traded the canvas for a sofa. The painting now hangs in New York’s Museum of Modern Art. The last so-called “Ferus Type” Elvis to appear at auction — Warhol made 23 of them in total — was sold at Christie’s for $53 million in May. On the fate of the sofa, the record is silent.

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There has long existed an informal system of exchange between creative people, a reciprocity born of mutual admiration, camaraderie or rivalry — and sometimes, a potently ambivalent mix of all three. Pablo Picasso traded work with his great frenemy Henri Matisse; Paul Gauguin with Vincent van Gogh. Paul Klee and Wassily Kandinsky, devoted friends, gave each other small paintings for birthdays and Christmas. Francis Bacon and Lucian Freud, combative yet close for 25 years, exchanged portraits they’d made of each other before they finally had an irreparable falling out. Swapping work, even for the fondest of pals, can be tricky: There’s ego involved, and the fear of rejection, not to mention logistical concerns of transport and storage; with the middleman eliminated, the rules tend to be fluid, sometimes unnervingly so, given the vertiginous stakes of the commercial art market. Who’s to say whose work will be worth more in a dozen years? Works of art, as Gertrude Stein famously said, are always either priceless or worthless.