Mathematical Definition
A cooperative game is given by specifying a value for every coalition. Formally, the game (coalitional game) consists of a finite set of players, called the grand coalition, and a characteristic function from the set of all possible coalitions of players to a set of payments that satisfies . The function describes how much collective payoff a set of players can gain by forming a coalition, and the game is sometimes called a value game or a profit game. The players are assumed to choose which coalitions to form, according to their estimate of the way the payment will be divided among coalition members.
Conversely, a cooperative game can also be defined with a characteristic cost function satisfying . In this setting, players must accomplish some task, and the characteristic function represents the cost of a set of players accomplishing the task together. A game of this kind is known as a cost game. Although most cooperative game theory deals with profit games, all concepts can easily be translated to the cost setting.
Read more about this topic: Cooperative Game
Famous quotes containing the words mathematical and/or definition:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)