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arXiv · 2209.15151

Tight Inapproximability for Graphical Games

Argyrios Deligkas·John Fearnley·Alexandros Hollender·Themistoklis Melissourgos
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Abstract

We provide a complete characterization for the computational complexity of finding approximate equilibria in two-action graphical games. We consider the two most well-studied approximation notions: $\varepsilon$-Nash equilibria ($\varepsilon$-NE) and $\varepsilon$-well-supported Nash equilibria ($\varepsilon$-WSNE), where $\varepsilon \in [0,1]$. We prove that computing an $\varepsilon$-NE is PPAD-complete for any constant $\varepsilon < 1/2$, while a very simple algorithm (namely, letting all players mix uniformly between their two actions) yields a $1/2$-NE. On the other hand, we show that computing an $\varepsilon$-WSNE is PPAD-complete for any constant $\varepsilon < 1$, while a $1$-WSNE is trivial to achieve, because any strategy profile is a $1$-WSNE. All of our lower bounds immediately also apply to graphical games with more than two actions per player.

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BibTeXRIS

Argyrios Deligkas, John Fearnley, Alexandros Hollender, Themistoklis Melissourgos. 2022-09-30. Tight Inapproximability for Graphical Games. https://arxiv.org/abs/2209.15151

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