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Equilibrium Points of Bimatrix Games
Abstract
An algebraic proof is given of the existence of equilibrium points for bimatrix (or two-person, non-zero-sum) games. The proof is constructive, leading to an efficient scheme for computing an equilibrium point. In a nondegenerate case, the number of equilibrium points is finite and odd. The proof is valid for any ordered field.
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Citations
Cited by
Multiagent systems: algorithmic, game-theoretic, and logical foundations
(2009) · Choice Reviews Online · doi:10.5860/choice.46-5662 · Cited by 1,756
The complexity of computing a Nash equilibrium
Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H. (2006) · Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing · doi:10.1145/1132516.1132527 · Cited by 470
A new method for a class of linear variational inequalities
He, B. (1994) · Mathematical Programming · doi:10.1007/bf01581141 · Cited by 162
Metadata
- Authors
- Lemke, C. E., & Howson, Jr.
- Venue
- Journal of the Society for Industrial and Applied Mathematics
- Published
- 1964-06
- Volume
- 12
- Issue
- 2
- Pages
- 413-423
- ISSN
- 0368-4245 (ISSN-L)
- 2168-3484
- OpenAlex
- W2089649903
- Cited by
- 1,231
- References
- 0
- FWCI
- 1.65
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Equilibrium Points of Bimatrix Games. https://app.cochat.ai/papers/10.1137/0112033
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- Lemke, C. E., & Howson, Jr. (1964). Equilibrium Points of Bimatrix Games. Journal of the Society for Industrial and Applied Mathematics. https://doi.org/10.1137/0112033
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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.
