TY - JOUR
AU - Deligkas, Argyrios
AU - Fearnley, John
AU - Hollender, Alexandros
AU - Melissourgos, Themistoklis
PY - 2023/06/26
Y2 - 2024/04/18
TI - Tight Inapproximability for Graphical Games
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 37
IS - 5
SE - AAAI Technical Track on Game Theory and Economic Paradigms
DO - 10.1609/aaai.v37i5.25695
UR - https://ojs.aaai.org/index.php/AAAI/article/view/25695
SP - 5600-5607
AB - 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 is in [0,1]. We prove that computing an ε-NE is PPAD-complete for any constant ε smaller than 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 smaller than 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.
ER -