caa a22 4500 477048358 CHVBK 20180405111336.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF01254380 doi (NATIONALLICENCE)springer-10.1007/BF01254380 A generalization of the Nash equilibrium theorem on bimatrix games [Elektronische Daten] [M. Seetharama Gowda, Roman Sznajder] In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games. Physica-Verlag, 1996 Bimatrix game nationallicence ɛ-equilibrium nationallicence optimal strategies nationallicence vertical linear complementarity problem nationallicence degree nationallicence stability nationallicence Seetharama Gowda M. Department of Mathematics and Statistics, University of Maryland, 21228, Baltimore County, Baltimore, Maryland, USA aut Sznajder Roman Department of Mathematics and Statistics, University of Maryland, 21228, Baltimore County, Baltimore, Maryland, USA aut International Journal of Game Theory Physica-Verlag 25/1(1996-03-01), 1-12 0020-7276 25:1<1 1996 25 182 https://doi.org/10.1007/BF01254380 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01254380 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Seetharama Gowda M. Department of Mathematics and Statistics, University of Maryland, 21228, Baltimore County, Baltimore, Maryland, USA aut NATIONALLICENCE 700 1- Sznajder Roman Department of Mathematics and Statistics, University of Maryland, 21228, Baltimore County, Baltimore, Maryland, USA aut NATIONALLICENCE 773 0- International Journal of Game Theory Physica-Verlag 25/1(1996-03-01), 1-12 0020-7276 25:1<1 1996 25 182 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer