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arXiv · 2103.03238

On the Complexity of Equilibrium Computation in First-Price Auctions

Aris Filos-Ratsikas·Yiannis Giannakopoulos·Alexandros Hollender·Philip Lazos·Diogo Poças
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Abstract

We consider the problem of computing a (pure) Bayes-Nash equilibrium in the first-price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the value distributions of the other bidders, computing an $\varepsilon$-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete. We also provide an efficient algorithm for solving a special case of the problem, for a fixed number of bidders and available bids.

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Aris Filos-Ratsikas, Yiannis Giannakopoulos, Alexandros Hollender, Philip Lazos, Diogo Poças. 2021-03-04. On the Complexity of Equilibrium Computation in First-Price Auctions. https://doi.org/10.1137/21m1435823

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