Auction

google

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late 16th century: from Latin auctio(n- ) ‘increase, auction’, from the verb augere ‘to increase’.

wiktionary

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From Latin auctiō(“an increase, auction”), from Latin augere(“to increase”).

etymonline

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auction (n.)

"public sale in which each bidder offers more than the previous bid," 1590s, from Latin auctionem (nominative auctio) "a sale by increasing bids, public sale," noun of action from past-participle stem of augere "to increase," from PIE root *aug- (1) "to increase." In northern England and Scotland, called a roup. In the U.S., something is sold at auction; in England, by auction.

auction (v.)

"sell by auction," by 1723 (implied in auctioned), from auction (n.). Since early 19c., commonly with off (adv.). Related: Auctioning.