by Constantinos Daskalakis, Paul W. Goldberg, Christos H. Papadimitriou
http://www.cs.berkeley.edu/~christos/papers/ppad.ps
Add To MetaCart
Abstract:
We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomialtime solvability of normal-form games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPAD-complete class of Brouwer functions. 1
Citations
|
673
|
A Course in Game Theory
– Osborne, Rubinstein
- 1994
|
|
342
|
Non-cooperative games
– Nash
- 1951
|
|
124
|
Graphical models for game theory
– Kearns, Littman, et al.
- 2001
|
|
92
|
On the complexity of the parity argument and other inefficient proofs of existence
– Papadimitriou
- 1994
|
|
87
|
Complexity results about Nash equilibria
– Conitzer, Sandholm
- 2003
|
|
79
|
Nash and correlated equilibria: Some complexity considerations, Games and Economic Behavior 1:80–93
– Gilboa, Zemel
- 1989
|
|
46
|
The complexity of pure nash equilibria
– Fabrikant, Papadinitriou, et al.
- 2004
|
|
28
|
Exponential Lower Bounds for Finding Brouwer Fixed Points
– Hirsch, Vavasis, et al.
- 1989
|
|
19
|
Exponentially many steps for finding a nash equilibrium in a bimatrix game
– Savani, Stengel
|
|
13
|
Nash equilibria via polynomial equations
– Lipton, Markakis
- 2004
|
|
12
|
Leontieff economies encode nonzero sum two-player games
– Codenotti, Saberi, et al.
- 2006
|
|
6
|
Reducibility Among Equilibrium
– Goldberg, Papadimitriou
- 2005
|
|
4
|
Nash and Walras Equilibrium via Brouwer,” Economic Theory
– Geanakoplos
- 2003
|
|
4
|
Computing Correlated Equilibria
– Papadimitriou
- 2005
|
|
4
|
The Computational Complexity of Nash Equilibria
– Schoenebeck, Vadhan
- 2005
|
|
3
|
How Easy is Local
– Johnson, Papadimitriou, et al.
|
|
2
|
An Efficient Exact Algorithm for Single Connected Graphical Games
– Littman, Kearns, et al.
- 2002
|
