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Mechanism Design with Spiteful Agents

Aditya Aradhye, David Lagziel, Eilon Solan

TL;DR

This paper investigates mechanism design when agents exhibit spiteful preferences that aim to hurt others given their own payoff. It develops a Spite-Free Nash Equilibrium framework and proves that IR and IC mechanisms admitting such an equilibrium are exactly threshold mechanisms, with two key impossibility results showing that anonymity or efficiency forces the mechanism to be null. It extends the analysis to multi-item settings, introducing cluster and sequential threshold extensions and examining conditions under which SIC can be maintained, especially for homogeneous, submodular valuations. The results reveal intrinsic challenges in auction design under other-regarding preferences and establish a rigorous threshold-based characterization that guides spite-resilient mechanism design.

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.

Mechanism Design with Spiteful Agents

TL;DR

This paper investigates mechanism design when agents exhibit spiteful preferences that aim to hurt others given their own payoff. It develops a Spite-Free Nash Equilibrium framework and proves that IR and IC mechanisms admitting such an equilibrium are exactly threshold mechanisms, with two key impossibility results showing that anonymity or efficiency forces the mechanism to be null. It extends the analysis to multi-item settings, introducing cluster and sequential threshold extensions and examining conditions under which SIC can be maintained, especially for homogeneous, submodular valuations. The results reveal intrinsic challenges in auction design under other-regarding preferences and establish a rigorous threshold-based characterization that guides spite-resilient mechanism design.

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.

Paper Structure

This paper contains 26 sections, 12 theorems, 25 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related work
  3. The structure of the paper
  4. The Model
  5. Simple properties of mechanisms
  6. A notion of spitefulness
  7. Characterizing Spite-Free mechanisms
  8. Main result
  9. Efficient and Anonymous Spite-Free mechanisms
  10. Extensions and Open problems
  11. Efficiency of the threshold mechanism
  12. Extension to a multi-item setting
  13. The updated model
  14. Two extensions of threshold mechanisms
  15. Homogeneous items and submodular valuations
  16. ...and 11 more sections

Key Result

Lemma 1

Figures (3)

  • Figure 1: A two-agent threshold mechanism represented in the valuation plane. The thresholds of the two agents are $t_1$ and $t_2$, respectively. If agent $1$ bids above her threshold $t_1$, she receives the item and pays $t_1$. Otherwise, the item is allocated to agent $2$, provided that her bid exceeds $t_2$, in which case she pays $t_2$.
  • Figure 2: The partition of the valuation space into the sets $(V_1^T(b_2))_{T \subseteq \{a_1,a_2\}}$ for a given $b_2$.
  • Figure 3: The relations between bid profiles $b$, $b'$, $c$, and $c'$.

Theorems & Definitions (24)

  • Lemma 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Theorem 2
  • Lemma 2
  • proof
  • ...and 14 more