On the Complexity of Equilibrium Computation in First-Price Auctions

4 Mar 2021 · Aris Filos-Ratsikas, Yiannis Giannakopoulos, Alexandros Hollender, Philip Lazos, Diogo Poças ·

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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On the Complexity of Equilibrium Computation in First-Price Auctions

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