Tight Inapproximability for Graphical Games

Deligkas, A, Fearnley, J, Hollender, A and Melissourgos, T
(2023) Tight Inapproximability for Graphical Games. In: AAAI 2023.

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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: ε-Nash equilibria (ε-NE) and ε-well-supported Nash equilibria (ε-WSNE), where ε ∈ [0, 1]. We prove that computing an ε-NE is PPAD-complete for any constant ε < 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 ε-WSNE is PPAD-complete for any constant ε < 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.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 22 Nov 2022 16:53
Last Modified: 24 Nov 2023 03:00
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3166323