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Difference between revisions of "Coalition"

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====Comments====
 
====Comments====
Formally, in an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022750/c0227501.png" />-player game a coalition is a non-empty subset of the set of players <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022750/c0227502.png" /> (a group of players). The set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022750/c0227503.png" /> 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.
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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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022750/c0227504.png" />. (See also [[#References|[a1]]].)
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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
This article was adapted from an original article by A.S. Mikhailova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article