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The Generalized Second Price auction is the primary method by which sponseredsearch advertisements are sold. We study the performance of this auction undervarious equilibrium concepts. In particular, we demonstrate that the BayesianPrice of Anarchy is at most $2(1-1/e)^{-1} \approx 3.16$, significantlyimproving upon previously known bounds.  Our techniques are intuitively straightforward and extend in a number ofways. For one, our result extends to a bound on the performance of GSP atcoarse correlated equilibria, which captures (for example) a repeated-auctionsetting in which agents apply regret-minimizing bidding strategies. Inaddition, our analysis is robust against the presence of byzantine agents whocannot be assumed to participate rationally.  Additionally, we present tight bounds for the social welfare obtained at pureNE for the special case of an auction for 3 slots, and discuss potentialmethods for extending this analysis to an arbitrary number of slots.

Improved Social Welfare Bounds for GSP at Equilibrium