Resumen de On the convenience to form coalitions or partnerships in simple games

Maria Dolors Llongueras Arola, Francesc Carreras Escobar

• Kalai and Samet (1987) introduced the concept of partnership in cooperative games. A partnership is a coalition that has an internal structure and, simultaneously, behaves as an individual member.

  Furthermore, when one o more players decide to form a coalition a coalition structure (i.e. a partition) arises and the quotient game is defined.

  In this work the Shapley and Banzhaf values are used to describe the convenience to form either coalitions or partnerships in a simple game. In fact, the difference between the Shapley (and Banzhaf) value for the partnership players and for their representative in the quotient game is analyzed. Maximum and minimum values for this difference are established.

  Finally, partnership and coalition structure imposition are studied in weighted majority games, a fraction of simple games.