New Core-Selecting Payment Rules with Better Fairness and Incentive Properties ̊

In this paper, we study the design of core-selecting payment rules for combinatorial auctions (CAs), a challenging setting where no strategyproof rules exist. We observe that in many real-world CAs, bidders are heterogeneous in size and value. Unfortunately, the rule most commonly used in practice, the Quadratic rule (Day and Cramton, 2012), significantly favors large over small bidders in terms of incentives as well as expected payoffs; this remains true even when normalizing to VCG payoffs. We first show analytically that in the Bayes-Nash equilibrium of the LLG domain, chosen here as in previous work for its tractably small size, the VCG-Discount-Small rule provides both much better incentives than the Quadratic rule and a fairer payoff distribution (as measured by our newly-defined Gini coefficents for payment rules). In a second step, we develop a general framework to design 75 new, and specify 9 existing, core-selecting rules built around different distance metrics, reference points, and bidder weightings. To measure the performance of these rules in realistically-sized CAs, we then develop a computational approach for finding approximate Bayes-Nash equilibria in CAs. We use this approach to study our rules in CAs with up to 25 items and 10 bidders. Based on this analysis, we ultimately recommend using one of our new rules: the Marginal-Economy-Fractional rule with VCG as the reference point. We find that this rule generally performs as well as or even slightly better than the Quadratic rule in terms of efficiency and revenue, but significantly improves upon it in terms of aggregate incentives and fairness.