Mechanism Design with Spiteful Agents

TL;DR

This paper characterizes mechanisms resilient to spiteful agents in single and multi-item settings, revealing fundamental limitations like the collapse to null mechanisms under certain conditions.

Contribution

It provides a complete characterization of IR and IC mechanisms immune to spite, and proves key impossibility results in auction design with spiteful agents.

Findings

IR and IC mechanisms are threshold-based with agent ordering

Under anonymity or efficiency, such mechanisms reduce to null mechanisms

Extends analysis to multi-item scenarios

Abstract

We study a mechanism-design problem in which spiteful agents strive to not only maximize their rewards but also, contingent upon their own payoff levels, seek to lower the opponents' rewards. We characterize all individually rational (IR) and incentive-compatible (IC) mechanisms that are immune to such spiteful behavior, showing that they take the form of threshold mechanisms with an ordering of the agents. Building on this characterization, we prove two impossibility results: under either anonymity or efficiency, any such IR and IC mechanism collapses to the null mechanism, which never allocates the item to any agent. Leveraging these findings, we partially extend our analysis to a multi-item setup. These results illuminate the challenges of auctioning items in the natural presence of other-regarding preferences.