In discretized first-price auctions, online gradient ascent by buyers produces time-average outcomes that match the efficient allocation of the second-price auction.
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A condensed time-expanded network with O(n²μ) nodes and O(μmn) edges solves max flow over time with μ capacity changes in O(μ²n³m) time.
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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.
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Brief announcement: A special case of maximum flow over time with network changes
A condensed time-expanded network with O(n²μ) nodes and O(μmn) edges solves max flow over time with μ capacity changes in O(μ²n³m) time.