VickreyClarkeGrovesmekanismerna

The Vickrey-Clarke-Groves (VCG) mechanism is a family of truthful, welfare-maximizing mechanisms in economic theory. Named after William Vickrey, Edward Clarke, and Theodore Groves, it generalizes the concept of a second-price auction to settings with multiple agents and more complex outcome spaces, such as combinatorial allocations.

In a setting with agents i each holding private valuations v_i(o) for outcomes o, the mechanism selects an outcome a* that maximizes the sum of valuations (social welfare). Each agent pays a transfer p_i designed so that truth-telling is a dominant strategy. A standard form uses the Clarke pivot rule: p_i = h_i(v_{-i}) - sum_{j≠i} v_j(a*), where h_i(v_{-i}) is the maximum welfare achievable by others without i. Intuition: an agent pays the externality its participation imposes on others.

Properties: The mechanism is efficient, selecting the welfare-maximizing outcome, and strategyproof, meaning agents maximize their utility by reporting truthfully regardless of others’ reports. It is not generally budget-balanced; the total payments may not sum to zero, and a surplus or deficit can arise. It assumes quasi-linear utilities and sufficient computational capability to determine welfare-maximizing outcomes.

Applications and limitations: VCG mechanisms are used in combinatorial auctions, public good provision, and other settings requiring truthful revelation of preferences. They rely on the ability to compute optimal allocations and can be vulnerable to strategic collusion or false-name bidding. They may also suffer from computational complexity in large problems and are not guaranteed to be budget-balanced.

Special case: For single-item auctions with two bidders, the VCG mechanism reduces to the standard second-price (Vickrey) auction, where the highest bidder wins and pays the second-highest bid.