Models for Cooperative Games with Fuzzy Relations among the Agents by Andrés Jiménez-Losada

Author:Andrés Jiménez-Losada
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Now, by Theorem 1.​1

Finally, following Definition 3.​6, we see that . In fact, for any coalition S we have , and then since Definition 3.​5

The last equality in the proposition is given by (4.1).

In order to find an axiomatization of the Myerson value we take into account that players are asymmetric in the structure because in each component the situation of the players contained in it is different, for instance the position of player 1 in Fig. 4.5 is not the same of players 2, 3. Therefore equal treatment of players in the same component (symmetry) is not possible. Myerson [9] used then an axiomatization based in a fairness axiom, thinking about the deletion of a link by Definition 4.6. Let a value for games over N with coalition structure.

Efficiency by components. If and then for all .

Fairness. Let and , it holds for all that

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