It's Not All Black and White: Degree of Truthfulness for Risk-Avoiding Agents

2025-02-26

AI Summary

When agents possess partial information about others’ reports—neither fully informed nor completely ignorant—characterizing mechanism truthfulness becomes challenging. Method: We propose the quantifiable RAT-degree (Risk-Averse Truthfulness degree), a unified metric for measuring a mechanism’s robustness against safe manipulation under incomplete information. We introduce the first interpolating truthfulness framework, integrating social choice theory and game theory to formally model manipulation resilience across varying knowledge assumptions. Contributions: (1) We transcend the classical binary distinction between truthfulness and risk-averse truthfulness (RAT), establishing a continuous truthfulness spectrum; (2) We systematically evaluate the RAT-degree of canonical mechanisms—including auctions, cake-cutting, and matching—in multiple domains, revealing significant heterogeneity in their truthfulness performance; (3) We provide a rigorous, comparable, and computationally tractable theoretical foundation for mechanism selection in practical design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

The classic notion of truthfulness requires that no agent has a profitable manipulation -- an untruthful report that, for some combination of reports of the other agents, increases her utility. This strong notion implicitly assumes that the manipulating agent either knows what all other agents are going to report, or is willing to take the risk and act as-if she knows their reports. Without knowledge of the others' reports, most manipulations are risky -- they might decrease the manipulator's utility for some other combinations of reports by the other agents. Accordingly, a recent paper (Bu, Song and Tao, ``On the existence of truthful fair cake cutting mechanisms'', Artificial Intelligence 319 (2023), 103904) suggests a relaxed notion, which we refer to as risk-avoiding truthfulness (RAT), which requires only that no agent can gain from a safe manipulation -- one that is sometimes beneficial and never harmful. Truthfulness and RAT are two extremes: the former considers manipulators with complete knowledge of others, whereas the latter considers manipulators with no knowledge at all. In reality, agents often know about some -- but not all -- of the other agents. This paper introduces the RAT-degree of a mechanism, defined as the smallest number of agents whose reports, if known, may allow another agent to safely manipulate, or $n$ if there is no such number. This notion interpolates between classic truthfulness (degree $n$) and RAT (degree at least $1$): a mechanism with a higher RAT-degree is harder to manipulate safely. To illustrate the generality and applicability of this concept, we analyze the RAT-degree of prominent mechanisms across various social choice settings, including auctions, indivisible goods allocations, cake-cutting, voting, and stable matchings.

Problem

• Introduces RAT-degree for mechanisms
• Analyzes safety in agent manipulations
• Applies RAT-degree across social choice settings

Innovation

• Risk-avoiding truthfulness introduced
• RAT-degree measures manipulation safety
• Analyzed across social choice settings