On the Complexity of Equilibrium Computation in First-Price Auctions

03/04/2021

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by   Aris Filos-Ratsikas, et al.

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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 ε-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete.