@inproceedings{982b49979a9e4d549a2c403739172852,

title = "Settling some open problems on 2-player symmetric nash equilibria",

abstract = "Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #Pcomplete. In 2005, Kannan and Theobald defined the rank of a bimatrix game represented by matrices (A,B) to be rank(A + B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann{\textquoteright}s reduction of such games to linear programming. In 2011, Adsul et al. obtained an algorithm for rank 1 games; however, it does not guarantee symmetric NE in symmetric rank 1 game. We resolve this problem.",

author = "Ruta Mehta and Vazirani, {Vijay V.} and Sadra Yazdanbod",

year = "2015",

month = jan,

day = "1",

doi = "10.1007/978-3-662-48433-3_21",

language = "English (US)",

isbn = "9783662484326",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "272--284",

editor = "Martin Hoefer and Martin Hoefer",

booktitle = "Algorithmic Game Theory - 8th International Symposium, SAGT 2015",

note = "8th International Symposium on Algorithmic Game Theory, SAGT 2015 ; Conference date: 28-09-2015 Through 30-09-2015",

}