The Complexity of Min-Max Optimization with Product Constraints
Year: 2026
Type: preprint
Abstract: We study the computational complexity of the problem of computing local min-max equilibria of games with a nonconvex-nonconcave utility function $f$. From the work of Daskalakis, Skoulakis, and Zampetakis [DSZ21], this problem was known to be hard in the restrictive case in which players are required to play strategies that are jointly constrained, leaving open the question of its complexity under more natural constraints. In this paper, we settle the question and show that the problem is PPAD-hard even under product constraints and, in particular, over the hypercube.
Source: arXiv (Cornell University)
Authors: Bernasconi, Martino, Castiglioni, Matteo
Institutions: Bocconi University, Politecnico di Milano
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7128016483