In discretized first-price auctions, online gradient ascent by buyers produces time-average outcomes that match the efficient allocation of the second-price auction.
2018.Cycles in Adversarial Regularized Learning
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Gradient Dynamics in First-Price Auctions: Iterative Strategy Elimination via Cubic Potentials
In discretized first-price auctions, online gradient ascent by buyers produces time-average outcomes that match the efficient allocation of the second-price auction.