Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. #R##N#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's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; hover, it does not solve the case of symmetric rank 1 games.  resolve this problem.
['Ruta Mehta', 'Vijay V. Vazirani', 'Sadra Yazdanbod']
I am writing a research paper on a idea Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
[{"from": "human", "value": "I am writing a research paper on a idea Settling Some Open Problems on 2-Player Symmetric Nash Equilibria"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. #R##N#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's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; hover, it does not solve the case of symmetric rank 1 games.  resolve this problem."}]