An empirical study of Fictitious Play for estimating Nash equilibria in first-price auctions with correlated values
For auction designers and researchers, this provides preliminary evidence that Fictitious Play can handle correlated values, but the results are incremental and call for further investigation.
This paper studies the computation of Nash equilibria in first-price auctions with correlated values, a setting where existing methods fail. Fictitious Play shows surprisingly good numerical convergence to ε-equilibrium across many instances.
This study concerns the computation of the Nash equilibria of first-price auctions with correlated values. Although some equilibrium computation methods exist for auctions with independent values, the correlation of bidders' values introduces significant complications that render the existing methods unsatisfactory. Our empirical contribution is a step towards filling this gap. We report surprisingly good numerical convergence of Fictitious Play toward an $\varepsilon$-equilibrium for an extensive set of instances. By doing so, we extend the insights of [39] to the correlated setting. These preliminary results call for further investigations into the properties of fictitious play algorithms on first-price auctions. 1. since the context is clear, we will use the term Nash equilibrium, or just equilibrium in this article