  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.
