The Complexity of Sparse Win-Lose Bimatrix Games

Eleni Batziou, John Fearnley, Abheek Ghosh and Rahul Savani

Papers from arXiv.org

Abstract: We prove that computing an $\epsilon$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $\epsilon$. Our result holds for 3-sparse games, which is tight given that 2-sparse win-lose bimatrix games can be solved in polynomial time.

Date: 2026-02
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