Paul Goldberg, Christos H. Papadimitriou

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 ...
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Xi Chen, Xiaotie Deng

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.

more >>>Constantinos Daskalakis, Christos H. Papadimitriou

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.

Xi Chen, Xiaotie Deng

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

more >>>Bruno Codenotti, Mauro Leoncini, Giovanni Resta

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 ...
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Xi Chen, Xiaotie Deng

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 >>>

Kord Eickmeyer, Kristoffer Arnsfelt Hansen, Elad Verbin

We consider the problem of approximating the minmax value of a multiplayer game in strategic form. We argue that in 3-player games with 0-1 payoffs, approximating the minmax value within an additive constant smaller than $\xi/2$, where $\xi = \frac{3-\sqrt5}{2} \approx 0.382$, is not possible by a polynomial time algorithm. ... more >>>

Anat Ganor, Karthik C. S.

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity of finding a 1/poly($N$)-approximate correlated equilibrium of the 2-cycle game is $\Omega(N)$. For ... more >>>