Auction Mechanisms: GSP vs VCG

Auction Mechanisms establish the game-theoretic rules determining ad slot allocations and settlement clearing prices among competing advertisers; the two dominant paradigms are: 1) GSP (Generalized Second Price Auction): ads are ranked by bid/eCPM, and the winner of slot $i$ pays the minimum price necessary to beat the $(i+1)$-th runner-up ($p_i = b_{i+1} + \epsilon$), representing the standard industrial deployment across Google and Baidu; 2) VCG (Vickrey-Clarke-Groves Auction): winners pay exactly the social cost/negative externality inflicted on all other bidders by occupying that slot, guaranteeing Truth-Telling (Dominant Strategy Incentive Compatibility, DSIC) as a dominant strategy.

Multi-slot sponsored search auctions, real-time programmatic ad exchanges, and display inventory auctions.

First-Price auctions incentivize continuous bid sniping and system oscillation; GSP and VCG establish stable game-theoretic equilibria encouraging rational, high-confidence advertiser valuation bids.

Derive the step-by-step VCG clearing price formula: $P_i = \sum_{j \neq i} v_j(S_{-i}^*) - \sum_{j \neq i} v_j(S^*)$ representing externalities?

Compare GSP vs VCG in multi-slot auctions: why does GSP fail strict Incentive Compatibility (truth-telling) across multiple slots?

Why do major platforms adopt GSP in production despite VCG's theoretical dominance (explaining explainability and platform revenue stability)?

Analyze Reserve Price design in GSP: Soft Floor vs Hard Floor tuning to maximize platform yield without depressing fill rate?

Analyze the modern resurgence of First-Price Auctions in header bidding and machine learning Bid Shading algorithms?