Guaranteed benefit collusion strategies for Vickrey–Clarke–Groves mechanism

Achieving socially optimal decisions requires access to agents’ true preferences, which is challenging as this information is privately held. The Vickrey–Clarke–Groves (VCG) mechanism addresses this problem by incentivizing truthful reporting when agents act individually. However, the mechanism is vulnerable to collusion, where agents form coalitions to manipulate the system for their own benefit. Although this weakness has been recognized in previous research, formal methods for guaranteed beneficial manipulation have remained elusive. This paper introduces four collusion strategies that guarantee benefits to coalitions. By characterizing these manipulation approaches, we develop modified VCG mechanisms that are robust against harmful collusion. Our contributions provide both a framework for understanding potential collusion strategies and practical mechanisms that maintain efficiency while resisting manipulation, making VCG more applicable in real-world settings where coalitions may form.