Designing Core-Selecting Payment Rules: A Computational Search Approach

Combinatorial auctions are regularly used to allocate resources worth billions of dollars. However, finding optimal payment rules for such auctions is still an open problem. To this end, we develop a new computational search framework for finding payment rules with desirable properties. We show that the rule most commonly used in practice, the quadratic rule, can be improved upon in terms of efficiency, incentives and revenue. Our best-performing rules are so-called large-style rules—that is, they provide better incentives to bidders with larger values. Ultimately, we identify two particularly well-performing rules and suggest that they be considered for practical implementation in place of the currently used rule. We study the design of core-selecting payment rules for combinatorial auctions, a challenging setting where no strategyproof rules exist. We show that the rule most commonly used in practice, the Quadratic rule, can be improved on in terms of efficiency, incentives, and revenue. We present a new computational search framework for finding good mechanisms, and we apply it toward a search for good core-selecting rules. Within our framework, we use an algorithmic Bayes–Nash equilibrium solver to evaluate 366 rules across 31 settings to identify rules that outperform the Quadratic rule. Our main finding is that our best-performing rules are large -style rules—that is, they provide bidders with large values with better incentives than does the Quadratic rule. Finally, we identify two particularly well-performing rules and suggest that they may be considered for practical implementation in place of the Quadratic rule. History: This paper has been accepted for the Information Systems Research Special Section on Market Design and Analytics. Ravi Bapna, Martin Bichler, Bob Day, Wolfgang Ketter, Senior Editors; Sasa Pekec, Associate Editor. Supplemental Material: The online supplement is available at https://doi.org/10.1287/isre.2022.1108 . Funding: Part of this research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme [Grant Agreement 805542]. This material is based upon work supported by the National Science Foundation [Grant CMMI-1761163].