The Complexity of Sparse Win-Lose Bimatrix Games

Eleni Batziou; John Fearnley; Abheek Ghosh; Rahul Savani

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arXiv · 2602.18380

The Complexity of Sparse Win-Lose Bimatrix Games

Eleni Batziou·John Fearnley·Abheek Ghosh·Rahul Savani

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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.

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BibTeX RIS

Eleni Batziou, John Fearnley, Abheek Ghosh, Rahul Savani. 2026-02-20. The Complexity of Sparse Win-Lose Bimatrix Games. https://arxiv.org/abs/2602.18380

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