Efficient Equilibrium Computation in Symmetric First-Price Auctions

TL;DR

This paper introduces the first efficient algorithms for computing Bayes-Nash equilibria in symmetric first-price auctions with i.i.d. bidders, addressing both continuous and finite bidding sets, and settling the problem's complexity.

Contribution

It provides the first polynomial-time and query-efficient algorithms for equilibrium computation in symmetric first-price auctions with i.i.d. bidders.

Findings

Polynomial-time algorithms for the white-box model.

Query-efficient algorithms for the black-box model.

Results settle the computational complexity for i.i.d. bidder values.

Abstract

We study the complexity of computing Bayes-Nash equilibria in single-item first-price auctions. We present the first efficient algorithms for the problem, when the bidders' values for the item are independently drawn from the same continuous distribution, under both established variants of continuous and finite bidding sets. More precisely, we design polynomial-time algorithms for the white-box model, where the distribution is provided directly as part of the input, and query-efficient algorithms for the black-box model, where the distribution is accessed via oracle calls. Our results settle the computational complexity of the problem for bidders with i.i.d. values.