Jurg, Peter; Jansen, Mathȳs; Tijs, Stef On pure equilibria for bimatrix games. (English) Zbl 0795.90087 Z. Oper. Res. 38, No. 2, 203-212 (1993). Summary: L. S. Shapley [Ann. Math. Stud. 52, 1-28 (1964; Zbl 0126.162)] gave several conditions for the existence of pure saddlepoints for a matrix game. We show that only a few of these conditions, when translated to the situation of a bimatrix game guarantee the existence of pure equilibria. Further, we associate with a bimatrix game a directed graph as well as a so-called ‘binary game’. If this graph has no cycles, then the bimatrix game in question has a pure equilibrium. It is shown that the binary game for a bimatrix game without a pure equilibrium possesses a ‘fundamental’ subgame, which can be characterized by means of ‘minimal’ cycles. MSC: 91A05 2-person games 91A43 Games involving graphs Keywords:minimal cycles; existence of pure saddlepoints; bimatrix game; pure equilibria; directed graph; binary game Citations:Zbl 0126.162 PDFBibTeX XMLCite \textit{P. Jurg} et al., Z. Oper. Res. 38, No. 2, 203--212 (1993; Zbl 0795.90087) Full Text: DOI References: [1] Shapley LS (1964) Some topics in two-person games. Ann of Math Stud 52:1-28 · Zbl 0126.16204 [2] Smadici C (1979) Generalized saddle points for bimatrix games. Proceedings of the Third Colloquium on Operations Research (Cluy-Napoca, 1978) Univ. ?Babes-Bolyai?, Cluy-Napoca 249-256 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.