Convergence-guaranteed equilibrium computation for correlated-value first-price auctions

Develop a methodology that guarantees convergence to an approximate Nash equilibrium in first-price auctions with correlated bidder values.

Background

The paper studies continuous-time fictitious play for symmetric two-bidder first-price auctions with independently distributed discrete values. It proves that, under a modified zero-on-tie rule and an admissibility assumption, fictitious play converges to a Nash equilibrium, and that this equilibrium is an approximate equilibrium for the standard uniform-split auction.

The introduction explicitly notes that a convergence-guaranteed methodology for computing approximate Nash equilibria in first-price auctions with correlated values has not yet been established. This problem is motivated by prior empirical observations that the modified tie-breaking approach appeared to converge across instances with correlated values, but the paper does not prove such a result.

References

Observe that a methodology that guaranties convergence to an estimate Nash equilibrium in first-price auction with correlated values is yet to be found, and that the empirical results from~\citet{heymann2025empirical} give hope that the methodology developed in this paper could further extend to some settings with correlated values.

— On the Role of Tie-Breaking Rules in the Convergence of Fictitious Play for Symmetric First-Price Auctions  (2609.18848 - Heymann, 16 Sep 2026) in Section 1, Introduction (footnote following the discussion of empirical results)