Difference between revisions of "Game situation"
From Encyclopedia of Mathematics
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| − | ''situation, | + | {{TEX|done}} |
| + | ''situation, $n$-tuple of strategies, in the theory of non-cooperative games'' | ||
| − | The result of a choice by all coalitions of action (see [[Games, theory of|Games, theory of]]) of their strategies with regard to the connections between the strategies of the various coalitions of action. The set of all situations can be understood as a subset of the Cartesian product | + | The result of a choice by all coalitions of action (see [[Games, theory of|Games, theory of]]) of their strategies with regard to the connections between the strategies of the various coalitions of action. The set of all situations can be understood as a subset of the Cartesian product $\prod_{K\in\mathfrak K_a}X_K$, where $X_K$ is the set of all strategies of the coalition of action $K$ and $\mathfrak K_a$ is the set of all coalitions of action. |
Revision as of 16:40, 18 October 2014
situation, $n$-tuple of strategies, in the theory of non-cooperative games
The result of a choice by all coalitions of action (see Games, theory of) of their strategies with regard to the connections between the strategies of the various coalitions of action. The set of all situations can be understood as a subset of the Cartesian product $\prod_{K\in\mathfrak K_a}X_K$, where $X_K$ is the set of all strategies of the coalition of action $K$ and $\mathfrak K_a$ is the set of all coalitions of action.
Comments
The notion of a game situation is hardly used in the Western literature.
How to Cite This Entry:
Game situation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Game_situation&oldid=13396
Game situation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Game_situation&oldid=13396
This article was adapted from an original article by A.S. Mikhailova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article