We address the fundamental question of whether the Nash equilibria of
a game can be computed in polynomial time. We describe certain
efficient reductions between this problem for
normal form games with a fixed number of players
and graphical games with fixed degree. Our main result is that ... more >>>

In this paper, we improve a recent result of Daskalakis, Goldberg and Papadimitriou on PPAD-completeness of 4-Nash, showing that 3-Nash is PPAD-complete.

We prove that computing a Nash equilibrium in a 3-player
game is PPAD-complete, solving a problem left open in our recent result on the complexity of Nash equilibria.

We prove that finding the solution of two player Nash Equilibrium is PPAD-complete.

It is known that finding a Nash equilibrium for win-lose bimatrix
games, i.e., two-player games where the players' payoffs are zero
and one, is complete for the class PPAD.

We describe a linear time algorithm which computes a Nash
equilibrium for win-lose bimatrix games where the number of winning
positions ... more >>>

While the 3-dimensional analogue of the Sperner problem in the plane was known to be PPAD-complete, the complexity of the 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, we settle this open problem proposed by Papadimitriou~\cite{PAP90} fifteen years ago. This also allows us to derive ... more >>>