Editing Cooperative game theory (section)

== Mathematical definition ==

A cooperative game is given by specifying a value for every coalition. Formally, the coalitional game consists of a finite set of players <math> N </math>, called the ''grand coalition'', and a ''characteristic function'' <math> v : 2^N \to \mathbb{R} </math> <ref><math>2^N</math> denotes the [[power set]] of <math>N</math>.</ref> from the set of all possible coalitions of players to a set of payments that satisfies <math> v( \emptyset ) = 0 </math>. The function describes how much collective payoff a set of players can gain by forming a coalition.