Difference between revisions of "Coalition"
From Encyclopedia of Mathematics
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| − | Formally, in an | + | Formally, in an $n$-player game a coalition is a non-empty subset of the set of players $P$ (a group of players). The set $P$ itself is sometimes called the "grand-coalitiongrand-coalition" . Usually there will be an argument in such a group concerning the choices to be made by the members of the group. In general the members will act jointly in such a way as to guarantee greater gain (cf. [[Gain function|Gain function]]) to themselves than they could ensure independently. |
| − | A coalition structure is a family of disjoint non-empty subsets of | + | A coalition structure is a family of disjoint non-empty subsets of $P$. (See also [[#References|[a1]]].) |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J. Szép, F. Forgó, "Introduction to the theory of games" , Reidel (1985)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> J.W. Friedman, "Oligopoly and the theory of games" , North-Holland (1977)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> J. Szép, F. Forgó, "Introduction to the theory of games" , Reidel (1985)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> J.W. Friedman, "Oligopoly and the theory of games" , North-Holland (1977)</TD></TR></table> | ||
Latest revision as of 07:31, 20 August 2014
(in the theory of games)
A group of persons or teams making a decision under conflict (a coalition of actions), or defending certain interests (a coalition of interests). See Games, theory of.
Comments
Formally, in an $n$-player game a coalition is a non-empty subset of the set of players $P$ (a group of players). The set $P$ itself is sometimes called the "grand-coalitiongrand-coalition" . Usually there will be an argument in such a group concerning the choices to be made by the members of the group. In general the members will act jointly in such a way as to guarantee greater gain (cf. Gain function) to themselves than they could ensure independently.
A coalition structure is a family of disjoint non-empty subsets of $P$. (See also [a1].)
References
| [a1] | J. Szép, F. Forgó, "Introduction to the theory of games" , Reidel (1985) |
| [a2] | J.W. Friedman, "Oligopoly and the theory of games" , North-Holland (1977) |
How to Cite This Entry:
Coalition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Coalition&oldid=33033
Coalition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Coalition&oldid=33033
This article was adapted from an original article by A.S. Mikhailova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article