Shapley-Based Core-Selecting Payment Rules

In this research note, we lay some groundwork for analyzing the manipulability of core-selecting payment rules in combinatorial auctions. In particular, we focus on payment rules based on the bidders' Shapley values. We define a sensitivity metric, and provide analytical results for this metric in LLG, for six different payment vectors used as reference points for minimum-revenue core-selecting payment rules. We furthermore show how this sensitivity affects the derivative of the resulting payment rules.