The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
The complexity of computing a Nash equilibrium
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 polynomial time solvability of normal form games and graphical games, establishing that these kinds of games can simulate a PPAD-complete class of Brouwer functions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
(1979) · Cited by 43,841
Theory of games and economic behavior
(2019) · 100 Years of Math Milestones · doi:10.1090/mbk/121/32 · Cited by 16,632
Nash, J. (1951) · The Annals of Mathematics · doi:10.2307/1969529 · Cited by 7,002
Linear Programming and Extensions
Dantzig, G. (1963) · RAND Corporation eBooks · doi:10.7249/r366 · Cited by 5,755
Nash, J. (1989) · Cournot Oligopoly · doi:10.1017/cbo9780511528231.007 · Cited by 5,595
(1994) · Cited by 5,513
The Theory of Games and Economic Behavior
Harrison, R. W., von Neumann, J., & Morgenstern, O. (1945) · Journal of Farm Economics · doi:10.2307/1232672 · Cited by 5,133
Polynomial algorithms in linear programming
Khachiyan, L. G. (1980) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(80)90061-0 · Cited by 1,992
Equilibrium Points of Bimatrix Games
Lemke, C. E., & Howson, Jr. (1964) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0112033 · Cited by 1,231
On the complexity of the parity argument and other inefficient proofs of existence
Papadimitriou, C. H. (1994) · Journal of Computer and System Sciences · doi:10.1016/s0022-0000(05)80063-7 · Cited by 778
Self-citation
Cited by
Multiagent systems: algorithmic, game-theoretic, and logical foundations
(2009) · Choice Reviews Online · doi:10.5860/choice.46-5662 · Cited by 1,756
Metadata
- Authors
- Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H.
- Venue
- Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
- Publisher
- ACM
- Published
- 2006-05-21
- Pages
- 71-78
- OpenAlex
- W2140790422
- Cited by
- 470
- References
- 33
- FWCI
- 80.24
- Type
- conference paper
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The complexity of computing a Nash equilibrium. https://app.cochat.ai/papers/10.1145/1132516.1132527
- The paper
- Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H. (2006). The complexity of computing a Nash equilibrium. Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing. https://doi.org/10.1145/1132516.1132527
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
