Profit Sharing Auction

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 nonwinning 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. Introduction Designers of agent societies are interested in constructing environments and interaction protocols that promote stable systems serving all individuals. Characteristics of desirable outcomes of multi-party interactions include stability and efficiency. Negotiation and coordination mechanisms that produce desirable outcomes have therefore been extensively studied in multiagent literature (Kraus 2001). General multiagent interaction protocols typically address issues of distribution of profits between all parties concerned. Other researchers, e.g., in cooperative game theory (Eichberger 1993) use concepts like Shapley value to promote fair distribution of profits between members of a group even though a Copyright c © 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. number of other distributions, including some with no profit for certain members, will maintain stability of the group1. One particular class of such multi-party negotiation protocols, viz., auctions, have been used in a variety of multiagent domains to facilitate transactions of goods and resources. Auctions have also received increased prominence with the success of popular Internet sites like eBay, uBid, etc. Multiagent researchers have both developed customizable auction sites, e.g., eMediator (Sandholm 2000), auctionBot (Wurman, Wellman, & Walsh 1998), etc., as well as investigated new auction protocols (Parkes 2001; Suyama & Yokoo 2004) and bidding strategies in different auction settings (Greenwald & Boyan 2005; Stone et al. 2003). The premise of this work is that one of the preferred goals of any multi-party protocol is social welfare distribution. More specifically, this dictates that if an interaction of many entities create a profit or surplus in the system, that amount should be distributed among the entities. Given that auctions are a particular class of multi-party interaction protocols, we can evaluate their effectiveness in view of the criterion of social welfare distribution. Now, one of the desired property accepted in auction theory is that of social welfare maximization. Let r be the reservation price of the seller of an item in any auction. Let B be the set of bidders in the auction. If vh is the highest valuation for the item among any bidder in the auction, then the maximum surplus that can be created by the interaction of the seller and the bidders B is vh − r, assuming all bidder valuations are drawn from the same distribution. This social welfare maximization is realized when the item is allocated to the highest bidder, winner, at any selling price, p, such that r ≤ p ≤ vh. This results in a profit of p − r for the seller and vh − p for the winner with all non-winning bidders receiving zero profit. The goal of social welfare distribution, however, would suggest, rather radically, some profit distribution among all bidders and the seller. While a philosophical debate about the desirability of social welfare distribution is beyond the scope of this paper, we briefly highlight two cases where such a distribution can be rationalized without axiomatic claims of the desirability Some payoff vectors in the core of the game may have zero payoff to some members.