Pure Nash Equilibria under the Affine Mechanism: A Potential Game of Exaggeration

2026-06-27

AI Summary

This study addresses the incentive incompatibility inherent in affine mechanisms—such as the mean mechanism—which incentivizes rational agents to misreport their true valuations. Within both complete-information and Bayesian game frameworks, the paper provides the first comprehensive characterization of the structure of pure-strategy Nash equilibria in such mechanisms, systematically modeling and solving for agents’ strategic behavior. The analysis establishes that, under broad conditions, agents inevitably adopt extremal overreporting strategies, and this behavior is unavoidable. Furthermore, the work derives necessary and sufficient conditions for the existence of pure-strategy Nash equilibria and explicitly constructs their forms, thereby uncovering the fundamental source of the intrinsic incentive flaws in affine mechanisms.

Abstract

The mean mechanism is known to be non-incentive-compatible, namely, rational players are incentivized to misreport their values. Despite this game-theoretic issue, the mean mechanism is prevalent in practice due to its other desirable properties. We give a full characterization of pure Nash equilibria--how the players will misreport--for the affine mechanism, of which the mean is a special case. Furthermore, we characterize both complete-information and Bayesian games under the affine mechanism. Our results highlight the inevitability of extreme exaggeration in such games.

Problem

• Pure Nash Equilibria
• Affine Mechanism
• Incentive Compatibility
• Exaggeration
• Mean Mechanism

Innovation

• affine mechanism
• pure Nash equilibria
• incentive compatibility
• strategic misreporting
• extreme exaggeration