New mathematical properties of the Banzhaf value

Article Abstract:

A new axiom describing a potential function for the Banzhaf value of a cooperative, transferable-utility game with a fixed set of players is introduced. The potential function enables the potential of the Banzhaf value to be derived in terms of the dividend form and the coalitional form of the game. Since the potential function's marginals are the elements of the Banzhaf value, games with an apriori given Banzhaf value may be explicitly represented in the space of all games with a fixed number of players.

Axioms

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Graphical solution of (n x m) matrix of a game theory

Article Abstract:

A new graphical method that can be applied for the (n x m) matrix of a game theory is proposed. Previous researches on the game theory of two players focused on the (n x 2) or (2 x m) matrix only. In the dominance property, the reduction method is more time consuming. Using the new method, the same problem can be solved graphically in only two steps. Thus, the new method is more convenient and easier to understand.

Usage, Graphic methods, Matrices, Matrices (Mathematics)

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