Auctions are a class of multi-party negotiation protocols. Classical auctions try to maximize social welfare by selecting the highest bidder as the winner. If bidders are rational, this ensures that the sum of profits for all bidders and the seller is maximized. In all such auctions, however, only the winner and the seller make any profit. We believe that ``social welfare distribution" is a desired goal of any multi-party protocol. In the context of auctions, this goal translates into a rather radical proposal of profit sharing between all bidders and the seller. We propose a Profit Sharing Auction (PSA) where a part of the selling price paid by the winner is paid back to the bidders. The obvious criticism of this mechanism is the incentive for the seller to share its profit with non-winning bidders. We claim that this loss can be compensated by attracting more bidders to such an auction, resulting in an associated increase in selling price. We run several sets of experiments where equivalent items are concurrently sold at a First Price Sealed Bid, a Vickrey, and a PSA auction. A population of learning bidders repeatedly choose to go to one of these auctions based on their valuation for the good being auctioned and their learned estimates of profits from these auctions. Results show that sellers make more or equivalent profits by using PSA as compared to the classical auctions. Additionally, PSA always attracts more bidders, which might create auxiliary revenue streams, and a desirable lower variability in selling prices. Interestingly then, a rational seller has the incentive to share profits and offer an auction like PSA which maximizes and distributes social welfare.