A heuristic for estimating Nash equilibria in first-price auctions with correlated values

TL;DR

This paper introduces a new heuristic called fictitious bidding for estimating Bayes-Nash equilibria in first-price auctions with correlated values, addressing the limitations of existing methods.

Contribution

The paper proposes a novel learning heuristic inspired by fictitious play to estimate equilibria in complex correlated-value auction models.

Findings

Fictitious bidding effectively estimates equilibria in various auction examples.

The heuristic outperforms traditional methods in correlated-value settings.

Results demonstrate practical applicability of the approach.

Abstract

Our paper concerns the computation of Nash equilibria of first-price auctions with correlated values. While there exist several equilibrium computation methods for auctions with independent values, the correlation of the bidders' values introduces significant complications that render existing methods unsatisfactory in practice. Our contribution is a step towards filling this gap: inspired by the seminal fictitious play process of Brown and Robinson, we present a learning heuristic-that we call fictitious bidding (FB)-for estimating Bayes-Nash equilibria of first-price auctions with correlated values, and we assess the performance of this heuristic on several relevant examples.