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We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player.
On the complexity of the parity argument and other inefficient proofs of existence
Christos H. Papadimitriou · 1994
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An efficient, exact algorithm for solving tree-structured graphical games
Michael L. Littman, Michael J. Kearns, and Satinder P. Singh · 2001
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Nash equilibria in graphical games on trees revisited
Edith Elkind, Leslie Ann Goldberg, and Paul W. Goldberg · 2006
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On the complexity of 2D discrete fixed point problem
Xi Chen and Xiaotie Deng · 2009
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Settling the complexity of computing two-player Nash equilibria
Xi Chen, Xiaotie Deng, and Shang-Hua Teng · 2009
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The complexity of computing a Nash equilibrium
Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou · 2009
Earlier work this paper cites.
On the complexity of Nash equilibria and other fixed points
Kousha Etessami and Mihalis Yannakakis · 2010
Cited alongside, same era.
On minmax theorems for multiplayer games
Yang Cai and Constantinos Daskalakis · 2011
Cited alongside, same era.
Approximating Nash equilibria in tree polymatrix games
Siddharth Barman, Katrina Ligett, and Georgios Piliouras · 2015
Cited alongside, same era.
An empirical study on computing equilibria in polymatrix games
Argyrios Deligkas, John Fearnley, Tobenna Peter Igwe, and Rahul Savani · 2016
Cited alongside, same era.
Settling the complexity of computing approximate two-player Nash equilibria
Aviad Rubinstein · 2016
Cited alongside, same era.
Computing constrained approximate equilibria in polymatrix games
Argyrios Deligkas, John Fearnley, and Rahul Savani · 2017
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Computing approximate Nash equilibria in polymatrix games
Argyrios Deligkas, John Fearnley, Rahul Savani, and Paul G. Spirakis · 2017
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Tractable algorithms for approximate Nash equilibria in generalized graphical games with tree structure
Luis E. Ortiz and Mohammad Tanvir Irfan · 2017
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Constant rank two-player games are PPAD-hard
Ruta Mehta · 2018
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Inapproximability of Nash equilibrium
Aviad Rubinstein · 2018
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