Learning Fair Equilibria in Sponsored Search Auctions

In this work we investigate the strategic learning implications of the deployment of sponsored search auction mechanisms that obey to fairness criteria. We introduce a new class of mechanisms composing a traditional Generalized Second Price auction (GSP) with different fair division schemes to achieve some desired level of fairness between two groups of Bayesian strategic advertisers. We propose two mechanisms, β-Fair GSP and GSP-EFX, that compose GSP with, respectively, an envy-free up to one item (EF1), and an envy-free up to any item (EFX) fair division scheme. The payments of GSP are adjusted in order to compensate the advertisers that suffer a loss of efficiency due the fair division stage. We prove that, for both mechanisms, if bidders play so as to minimize their external regret they are guaranteed to reach an equilibrium with good social welfare. We also prove that the mechanisms are budget balanced, so that the payments charged by the traditional GSP mechanism are a good proxy of the total compensation offered to the advertisers. Finally, we evaluate the quality of the allocations of the two mechanisms through experiments on real-world data.

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