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arXiv · 2303.16388

Complexity of Equilibria in First-Price Auctions under General Tie-Breaking Rules

Xi Chen·Binghui Peng
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Abstract

We study the complexity of finding an approximate (pure) Bayesian Nash equilibrium in a first-price auction with common priors when the tie-breaking rule is part of the input. We show that the problem is PPAD-complete even when the tie-breaking rule is trilateral (i.e., it specifies item allocations when no more than three bidders are in tie, and adopts the uniform tie-breaking rule otherwise). This is the first hardness result for equilibrium computation in first-price auctions with common priors. On the positive side, we give a PTAS for the problem under the uniform tie-breaking rule.

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Xi Chen, Binghui Peng. 2023-03-29. Complexity of Equilibria in First-Price Auctions under General Tie-Breaking Rules. https://arxiv.org/abs/2303.16388

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