Designing Core-selecting Payment Rules: A Computational Search Approach

We study the design of core-selecting payment rules for combinatorial auctions (CAs), a challenging setting where no strategyproof rules exist. Unfortunately, under the rule most commonly used in practice, the Quadratic rule Day and Cramton (2012), the equilibrium strategies are far from truthful. In this paper, we present a computational approach for nding good core-selecting payment rules. We present a parameterized payment rule we call FRACTIONAL∗ that takes three parameters (reference point, weights, and ampli cation) as inputs. This way, we construct and analyze 610 rules across 30 di erent domains. To evaluate each rule in each domain, we employ a computational Bayes-Nash equilibrium solver. We rst use our approach to study the well-known Local-Local-Global domain in detail, and identify a set of 20 “all-rounder rules” which beat Quadratic by a signi cant margin on e ciency, incentives, and revenue in all, or almost all domains. To demonstrate robustness of our ndings, we take four of these all-rounder rules and evaluate them in the signi cantly larger LLLLGG domain (with six bidders and eight goods), where we show that all four rules also beat Quadratic. Overall, our results demonstrate the power of a computational search approach in a mechanism design space, and more speci cally the large improvements that are possible over Quadratic.