Equilibrium Points in Bimatrix Games

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Previous article Next article Equilibrium Points in Bimatrix GamesN. N. Vorob’evN. N. Vorob’evhttps://doi.org/10.1137/1103024PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAn algorithm for computing all equilibrium points (situations) for the case of bimatrix (i.e., finite two-person, non-cooperative, non-zero-sum) games is given.[1] John Nash, Non-cooperative games, Ann. of Math. (2), 54 (1951), 286–295 MR0043432 0045.08202 CrossrefGoogle Scholar[2] L. S. Shapley and , R. N. Snow, Basic solutions of discrete gamesContributions to the Theory of Games, Annals of Mathematics Studies, no. 24, Princeton University Press, Princeton, N. J., 1950, 27–35 MR0039216 0041.25403 Google Scholar[3] David Blackwell and , M. A. Girshick, Theory of games and statistical decisions, John Wiley and Sons, Inc., New York, 1954xi+355 MR0070134 0056.36303 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Where Do Mistakes Lead? A Survey of Games with Incompetent Players10 February 2022 | Dynamic Games and Applications, Vol. 97 Cross Ref , Vol. 689 Cross Ref Sets of Nash Equilibria in Polymatrix Mixed-Strategy Games10 March 2018 Cross Ref Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game23 January 2017 | Applied Computer Systems, Vol. 20, No. 1 Cross Ref Ordered Field Property for Semi-Markov Games when One Player Controls Transition Probabilities and Transition TimesInternational Game Theory Review, Vol. 17, No. 02 Cross Ref ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMESInternational Game Theory Review, Vol. 15, No. 04 Cross Ref Incompetence and impact of training in bimatrix gamesAutomatica, Vol. 48, No. 10 Cross Ref Routing of Hazardous Material Shipments Under the Threat of Terrorist Attack12 January 2010 Cross Ref Enumeration of Nash equilibria for two-player games6 March 2009 | Economic Theory, Vol. 42, No. 1 Cross Ref A taxonomy of best-reply multifunctions in 2×2×2 trimatrix games21 September 2007 | TOP, Vol. 15, No. 2 Cross Ref A Taxonomy of Best-Reply Multifunctions in 2x2x2 Trimatrix GamesSSRN Electronic Journal Cross Ref Enumeration of All the Extreme Equilibria in Game Theory: Bimatrix and Polymatrix Games29 November 2006 | Journal of Optimization Theory and Applications, Vol. 129, No. 3 Cross Ref Hard-to-Solve Bimatrix GamesEconometrica, Vol. 74, No. 2 Cross Ref Solving three-player games by the matrix approach with application to an electric power marketIEEE Transactions on Power Systems, Vol. 18, No. 4 Cross Ref Tuning of discretization in bimatrix game approach to power system market analysisIEEE Transactions on Power Systems, Vol. 18, No. 2 Cross Ref Chapter 44 Non-zero-sum two-person games Cross Ref Chapter 45 Computing equilibria for two-person games Cross Ref Game Theory 1950–2000 Cross Ref Cooperation and self-interest: Pareto-inefficiency of Nash equilibria in finite random games18 August 1998 | Proceedings of the National Academy of Sciences, Vol. 95, No. 17 Cross Ref Pareto equilibria for bimatrix gamesComputers & Mathematics with Applications, Vol. 25, No. 10-11 Cross Ref On the structure of the set of perfect equilibria in bimatrix games1 March 1993 | Operations-Research-Spektrum, Vol. 15, No. 1 Cross Ref Un nuevo algoritmo para la resolucion de juegos bimatricialesTrabajos de Investigacion Operativa, Vol. 7, No. 1 Cross Ref Constructing bimatrix games with unique equilibrium pointsMathematical Social Sciences, Vol. 15, No. 1 Cross Ref B Cross Ref Maximal nash subsets for bimatrix gamesNaval Research Logistics Quarterly, Vol. 28, No. 1 Cross Ref Polymatrix Games with Joint ConstraintsB. Curtis Eaves17 February 2012 | SIAM Journal on Applied Mathematics, Vol. 24, No. 3AbstractPDF (489 KB)On the Set of Equilibria of a Bimatrix Game: a Survey Cross Ref Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game Cross Ref Equilibrium Points of Bimatrix GamesO. L. Mangasarian13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 4AbstractPDF (301 KB)Two-person nonzero-sum games and quadratic programmingJournal of Mathematical Analysis and Applications, Vol. 9, No. 3 Cross Ref Volume 3, Issue 3| 1958Theory of Probability & Its Applications History Submitted:12 March 1958Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1103024Article page range:pp. 297-309ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics