Editing Game theory (section)

===Characteristic function form===
{{main|Cooperative game theory}}
In cooperative game theory the characteristic function lists the payoff of each coalition. The origin of this formulation is in John von Neumann and Oskar Morgenstern's book.<ref>{{Cite web |date=2025-02-12 |title=Game theory - Von Neumann, Morgenstern, Theory {{!}} Britannica |url=https://www.britannica.com/science/game-theory/The-von-Neumann-Morgenstern-theory |access-date=2025-03-19 |website=Britannica |language=en}}</ref>

Formally, a characteristic function is a 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, and also satisfies <math> v( \emptyset ) = 0 </math>. The function describes how much collective payoff a set of players can gain by forming a coalition.