In many auctions, because of externalities, each bidder has a different maximum willingness to pay in order to beat each specific competitor, which causes the following new problem. When there are three bidders, two bidders might compete against each other unnecessarily and have worse payoffs than if they had lost to the third bidder, i.e., the two bidders have “group winner regret,” which can also lead to inefficiency. While no one-dimensional-bid mechanism is efficient, the Vickrey-Clarke-Groves may require losers to pay. This paper introduces a novel mechanism, the “multidimensional second-price” (MSP) auction (and its open ascending version), and characterizes it. MSP is free of a loser’s payment, pairwise stable, and has good incentive properties, including no group winner regret. Moreover, the winner cannot win at any different price by any misreport, and a loser cannot be better off winning by any misreport. MSP is strategyproof for a bidder without externalities imposed by others, and it reduces to the second-price auction when there are no externalities. Simulations suggest that MSP outperforms the second-price auction in terms of both revenue and efficiency.