Shapley-Based Core-Selecting Payment Rules

TL;DR

This paper investigates the manipulability of core-selecting payment rules in combinatorial auctions, focusing on Shapley value-based rules, and introduces a sensitivity metric to analyze their properties.

Contribution

It provides analytical results for the sensitivity of Shapley-based core payment rules and explores their impact on payment derivatives in combinatorial auctions.

Findings

Sensitivity metric defined and analyzed for Shapley-based rules

Analytical results for six reference payment vectors in LLG

Insights into how sensitivity influences payment rule derivatives

Abstract

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.