Improved Social Welfare Bounds for GSP at Equilibrium

The Generalized Second Price auction is the primary method by which sponsered search advertisements are sold. We study the performance of this auction under various equilibrium concepts. In particular, we demonstrate that the Bayesian Price of Anarchy is at most $2(1-1/e)^{-1} \approx 3.16$, significantly improving upon previously known bounds. Our techniques are intuitively straightforward and extend in a number of ways. For one, our result extends to a bound on the performance of GSP at coarse correlated equilibria, which captures (for example) a repeated-auction setting in which agents apply regret-minimizing bidding strategies. In addition, our analysis is robust against the presence of byzantine agents who cannot be assumed to participate rationally. Additionally, we present tight bounds for the social welfare obtained at pure NE for the special case of an auction for 3 slots, and discuss potential methods for extending this analysis to an arbitrary number of slots.

💡 Research Summary

The paper investigates the efficiency of the Generalized Second Price (GSP) auction, the dominant mechanism for selling sponsored search slots, under a variety of equilibrium concepts. Its primary contribution is a substantially tighter bound on the Bayesian Price of Anarchy (BPoA). By introducing a novel potential‑function framework together with a “price‑discount” transformation, the authors show that the worst‑case ratio between the optimal social welfare and the welfare achieved at any Bayesian Nash equilibrium is at most
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