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. We show that the rule most commonly used in practice, the Quadratic rule, can be improved upon in terms of efficiency, incentives and revenue. We present a new algorithm search framework for finding good mechanisms, and we apply it towards 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 Quadratic. Our main finding is that our best-performing rules are Large-style rules, i.e., they provide bidders with large values with better incentives than Quadratic. Finally, we identify two particularly well-performing rules and suggest that they may be considered for practical implementation in place of Quadratic.