Pure-Strategy Equilibrium in the Generalized First-Price Auction

Michael Ostrovsky; Andrzej Skrzypacz

Pure-Strategy Equilibrium in the Generalized First-Price Auction

Computer Science and Game Theory 2026-07-31 v1 Theoretical Economics

Authors: Michael Ostrovsky , Andrzej Skrzypacz

Abstract

We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the bids or on the product of bids and deterministic quality scores. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction, although under some conditions the relation may also be reversed.

Keywords

generalized first-price auction pure-strategy equilibrium sponsored search quality scores expected revenue

Cite

@article{arxiv.2608.00334,
  title  = {Pure-Strategy Equilibrium in the Generalized First-Price Auction},
  author = {Michael Ostrovsky and Andrzej Skrzypacz},
  journal= {arXiv preprint arXiv:2608.00334},
  year   = {2026}
}