TY - JOUR
AU - Fasoulakis, Michail
AU - Markakis, Evangelos
PY - 2019/07/17
Y2 - 2021/03/04
TI - An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 33
IS - 01
SE - AAAI Technical Track: Game Theory and Economic Paradigms
DO - 10.1609/aaai.v33i01.33011926
UR - https://ojs.aaai.org/index.php/AAAI/article/view/4020
SP - 1926-1932
AB - <p>We focus on the problem of <em>computing approximate Nash equilibria</em> in <em>bimatrix games</em>. In particular, we consider the notion of <em>approximate well-supported equilibria</em>, which is one of the standard approaches for approximating equilibria. It is already known that one can compute an <em>ε-well-supported</em> <em>Nash equilibrium</em> in time <em>n</em><sup>O (log <em>n/ε</em><sup>2</sup>)</sup>, for any <em>ε</em> > 0, in games with <em>n pure strategies</em> per player. Such a running time is referred to as <em>quasi-polynomial</em>. Regarding faster algorithms, it has remained an open problem for many years if we can have better running times for small values of the approximation parameter, and it is only known that we can compute in polynomial-time a 0<em>.</em>6528<em>-well-supported Nash equilibrium</em>. In this paper, we investigate further this question and propose a much better <em>quasi-polynomial time</em> algorithm that computes a (1<em>/</em>2 + <em>ε</em>)<em>-well-supported Nash equilibrium</em> in time <em>n</em><sup>O(log log<em>n</em>1/<em>ε</em>/<em>ε</em><sup>2</sup>), for any <em>ε ></em> 0. Our algorithm is based on appropriately combining sampling arguments, support enumeration, and solutions to systems of linear inequalities.</p>
ER -