# Coalition

*(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