Core of Balanced Family Games

ROBERTO P. ARRIBILLAGA

Congreso; IV Congreso Latinoamericano de Matemática; 2012

The balanced family games can be considered as an extension of the assignment games and are introduced in a similar way that the partitioning games studied by, Kaneko and Wooders (1982). Given a finite set N of players, there is an a priori given set π of coalitions of N and only coalitions in π play an essential role. The balanced family games propose that players could be organized towards overlapping coalitions structures take from π called balanced π-families. In contrast with partitioning game results, the balanced family games always have a non empty core extending with this a classical result of the assignment games. The core of the balanced families games is in accordance with ϵ-approximate cores of partitioning games, in fact the last ones tend to first ones when ϵ tends to zero.