{"type":"ScholarlyArticle","title":"Approximate Nash Equilibria with Near Optimal Social Welfare","authors":[{"name":"Artur Czumaj","slug":"artur-czumaj","given":"Artur","family":"Czumaj","affiliation":""},{"name":"Michail Fasoulakis","slug":"michail-fasoulakis","given":"Michail","family":"Fasoulakis","affiliation":""},{"name":"Marcin Jurdzinski","slug":"marcin-jurdzinski","given":"Marcin","family":"Jurdzinski","affiliation":""}],"abstract":"It is known that Nash equilibria and approximate Nash equilibria not necessarily optimize social optima of bimatrix games. In this paper, we show that for every fixed ε > 0, every bimatrix game (with values in [0, 1]) has an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor, (1 − √1 − ε)2, of the optimum. Furthermore, our result can be made algorithmic in the following sense: for every fixed 0 ≤ ε* < ε, if we can find an ε*-approximate Nash equilibrium in polynomial time, then we can find in polynomial time an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor of the optimum. Our analysis is especially tight in the case when ε ≥ 1/2. In this case, we show that for any bimatrix game there is an ε-approximate Nash equilibrium with constant size support whose social welfare is is at least 2√ε − ε ≥ 0.914 times the optimal social welfare. Furthermore, we demonstrate that our bound for the social welfare is tight, that is, for every ε ≥ 1/2 there is a bimatrix game for which every ε-approximate Nash equilibrium has social welfare at most 2√ε − ε times the optimal social welfare.","doi":null,"url":"https://ijcai.org/proceedings/2015/77","pdf":"https://ijcai.org/proceedings/2015/0077.pdf","markdown":"https://ijcai.org/proceedings/2015/77.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/77","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Game Theory","track":"Main Track","number":77,"pages":{"first":504,"last":509},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}