On pure equilibria for bimatrix games
Copyright policy )On pure equilibria for bimatrix games
Summary: \textit{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.
- Tilburg University Netherlands
- Radboud University Nijmegen Netherlands
Stochastics and operational research, bimatrix game, minimal cycles, binary game, Games involving graphs, directed graph, existence of pure saddlepoints, pure equilibria, 2-person games
Stochastics and operational research, bimatrix game, minimal cycles, binary game, Games involving graphs, directed graph, existence of pure saddlepoints, pure equilibria, 2-person games
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