Vickrey Auction

A sealed-bid auction where the highest bidder wins and pays the second-highest bid.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Winner: $i^*=\arg\max_j b_j$ ; payment: $p_{i^*}=\max_{j\ne i^*} b_j$ ; all others pay $0$ .

With single-unit private values, truthful bidding $b_i=v_i$ is weakly dominant.

Because price is set by others, your bid only affects whether you win, not how much you pay — so truth-telling is optimal.

Incentive compatibility means bidders do not need to strategize over others' valuations.

Values $(10,7,4)$ : bidder 1 wins and pays $7$ , netting surplus $3$ .

Under symmetric IPV, expected revenue equals that of the first-price auction (Revenue Equivalence).

The Vickrey auction is a special case of the VCG mechanism for a single indivisible good.

Generalizes to combinatorial settings as VCG, charging each winner their marginal externality on others.

Historical use in stamp auctions; conceptual basis for GSP in sponsored-search ads and many computerized markets.

Cornerstone example in mechanism-design teaching.

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.