Core-selecting combinatorial auctions (CAs) restrict the auction result in the core such that no coalitions could improve their utilities by engaging in collusion. The minimum-revenue-core (MRC) rule is a widely used core-selecting payment rule to maximize the total utilities of all bidders. However, the MRC rule can suffer from severe unfairness since it ignores individuals' utilities. To address this limitation, we propose to explore the leximin principle to achieve fairness in core-selecting CAs since the leximin principle prefers to maximize the utility of the worst-off; the resulting bidder-leximin-optimal (BLO) payment rule is then theoretically analyzed and an effective algorithm is further provided to compute the BLO outcome. Moreover, we conduct extensive experiments to show that our algorithm returns fairer utility distributions and is faster than existing algorithms of core-selecting payment rules.

翻译：核心选择组合拍卖将拍卖结果限制在核内，使得任何联盟都无法通过合谋提高自身效用。最低收入核规则是一种广泛采用的核心选择支付规则，旨在最大化所有投标人的总效用。然而，该规则可能因忽视个体效用而遭受严重的不公平性。为解决这一局限，我们提出探索Leximin原则以实现核心选择组合拍卖中的公平性——由于该原则优先最大化最差个体的效用，我们由此推导出投标人Leximin最优支付规则，并对其展开理论分析，进一步提供高效算法来计算BLO结果。此外，我们通过大量实验证明，该算法能返回更公平的效用分布，且速度优于现有的核心选择支付规则算法。