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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence / EAAI-20

An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria

February 1, 2023

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Authors

Michail Fasoulakis

Foundation for Research and Technology-Hellas


Evangelos Markakis

Athens University of Economics and Business


DOI:

10.1609/aaai.v33i01.33011926


Abstract:

We focus on the problem of computing approximate Nash equilibria in bimatrix games. In particular, we consider the notion of approximate well-supported equilibria, which is one of the standard approaches for approximating equilibria. It is already known that one can compute an ε-well-supported Nash equilibrium in time nO (log n/ε2), for any ε > 0, in games with n pure strategies per player. Such a running time is referred to as quasi-polynomial. 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 0.6528-well-supported Nash equilibrium. In this paper, we investigate further this question and propose a much better quasi-polynomial time algorithm that computes a (1/2 + ε)-well-supported Nash equilibrium in time nO(log logn1/ε/ε2), for any ε > 0. Our algorithm is based on appropriately combining sampling arguments, support enumeration, and solutions to systems of linear inequalities.

Topics: AAAI

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HOW TO CITE:

Michail Fasoulakis||Evangelos Markakis An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria Proceedings of the AAAI Conference on Artificial Intelligence (2019) 1926-1932.

Michail Fasoulakis||Evangelos Markakis An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria AAAI 2019, 1926-1932.

Michail Fasoulakis||Evangelos Markakis (2019). An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria. Proceedings of the AAAI Conference on Artificial Intelligence, 1926-1932.

Michail Fasoulakis||Evangelos Markakis. An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria. Proceedings of the AAAI Conference on Artificial Intelligence 2019 p.1926-1932.

Michail Fasoulakis||Evangelos Markakis. 2019. An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria. "Proceedings of the AAAI Conference on Artificial Intelligence". 1926-1932.

Michail Fasoulakis||Evangelos Markakis. (2019) "An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria", Proceedings of the AAAI Conference on Artificial Intelligence, p.1926-1932

Michail Fasoulakis||Evangelos Markakis, "An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria", AAAI, p.1926-1932, 2019.

Michail Fasoulakis||Evangelos Markakis. "An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria". Proceedings of the AAAI Conference on Artificial Intelligence, 2019, p.1926-1932.

Michail Fasoulakis||Evangelos Markakis. "An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria". Proceedings of the AAAI Conference on Artificial Intelligence, (2019): 1926-1932.

Michail Fasoulakis||Evangelos Markakis. An Improved Quasi-Polynomial Algorithm for Approximate Well-Supported Nash Equilibria. AAAI[Internet]. 2019[cited 2023]; 1926-1932.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
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