Shapley value based pricing for auctions and exchanges

This paper explores how the Shapley value can be used as the basis of a payment rule for auctions and exchanges. The standard Shapley value is modified so that losing bidders do not make or receive any payments. The new rule, called the balanced winner contribution (BWC) rule, satisfies a variation of Myerson's balanced contribution property. The payment rule is fair in the sense that, with respect to reported values, the members of every pair of traders make equal contributions to each other's share of the gains from trade. BWC payments can be used in single-item auctions and more complex auctions and exchanges with multiple items and package bidding. A series of examples is presented to illustrate how the BWC rule works and how the payments compare to those based on competitive prices, the core, and the Vickrey-Clarke-Groves mechanism.