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This study designs a new market for fractional ownership of autonomous vehicles (AVs), in which an AV is co‐leased by a group of individuals. We present a practical iterative auction based on the combinatorial clock auction to match the interested customers together and determine their payments. In designing such an auction, we consider continuous‐time items (time slots) that are defined by bidders and naturally exploit driverless mobility of AVs to form co‐leasing groups. To relieve the computational burdens of both bidders and the auctioneer, we devise user agents who generate packages and bid on behalf of bidders. Through numerical experiments using the California 2010–2012 travel survey, we test the performance of the auction design. We also compare various bidding strategies and study the effect of activity rules on the bidders' payoffs. We find that the designed activity rules successfully remove the strategic behavior of bidders. We also find that core‐selecting payment rule brings the largest revenue to the auctioneer in most cases. [ABSTRACT FROM AUTHOR]