Signed on a prefatory page in fountain pen by Tagore, the Bolpur edition of the book was published by The Macmillan Company in 1916.
The play revolves around a mysterious, unseen, omniscient king, who is both benevolent and efficient.
His reluctance towards being seen causes most of the drama in the story, rattling his beautiful wife and the kings of nearby kingdoms.
The book was consigned by an American book dealer, according to US-based RR Auction.
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Tagore became the first Indian to win a Nobel Prize (Literature) in 1913.
He wrote successfully in all literary genres, but was first and foremost a poet, publishing more than 50 volumes of poetry.
Tagore was knighted by the British in 1915, but gave up his knighthood after the Jallianwala Bagh massacre in 1919.
The bidding for the book ends on March 7.