Britannica Sources used in this answer

What is the characteristic-function form used for in game theory?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

A colorful payoff matrix for a normal form game in game theory, showing strategy options-support, oppose, evade-for both party A and party B. Each cell contains cartoon figures representing each party's action and lists percentage payoffs for A and B. The bottom-right cell is labeled saddlepoint, highlighting the equilibrium. — game theory Table 1
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.

In game theory, the characteristic-function form is primarily used to analyze games involving more than two players, particularly in the context of cooperative games.1

This form describes a game by identifying all possible coalitions of players—including individual players—and assigning each a value. This value represents the minimum amount that a specific coalition can guarantee for itself, assuming that the remaining players form a counter-coalition that acts to minimize the first coalition's payoff.12

By listing these values for every possible combination of players, the characteristic-function form provides a mathematical framework to study how players might join together to form groups and how they might distribute the resulting payoffs, often referred to as imputations. This approach was central to the work of John von Neumann and Oskar Morgenstern, who used it to develop a theory of n-person games based on the stability of these coalitions.2