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(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.


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].)


[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:
This article was adapted from an original article by A.S. Mikhailova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article