The principle of balanced contributions and hierarchies of cooperation

An implementation of the Owen value

“…Later, Calvo et al (1996) proved that also satisfies balanced contributions among players and coalitions.…”

“…Later, several authors extended other results of the Shapley value to the Owen value. Calvo, Lasaga, and Winter (1996) extended the results about balanced contributions, and Winter (1992) studied the results about the potential and consistency. Also, the Owen value has been used in cost allocation problems (Vázquez-Brage, van den Nouweland, and Garcia-Jurado (1997)) and political situations (Carreras and Owen (1988)).…”

Balanced per capita contributions and level structure of cooperation

“…In an even higher level, the EPP and the ED form a larger group, the EPP-ED, and other groups so forth. This example appears in Winter (1989), Calvo et al (1996) and Vidal-Puga (2005). In situations like this, a more detailed mapping of the cooperation structure is needed.…”

“…Calvo et al (1996) then provided a characterization of the level structure value using the principle of balanced contributions. This property states that, for any two coalitions that belong to the same coalition at higher levels, the amount that the players in each coalition would gain or lose by the other coalition's withdrawal from the game should be equal.…”

Implementation of the Levels Structure Value

“…A simple and powerful characterization for the levels structure value is as follows (Calvo, Lasaga, and Winter, 1996): the levels structure value is the only solution concept on LT U (N ) which satisfies efficiency and balanced contributions.…”