The Banzhaf interaction index for bi-cooperative games
Jabbar Abbas · International Journal of General Systems · 2021
The bipolar Möbius transform is an extension of dividends of cooperative games to that of bi-cooperative games. In this paper, we introduce the bipolar co-Möbius transform as an extension of co-Möbius transform of the cooperative game to that of bi-cooperative game. Then, we propose the Banzhaf interaction index among players in bi-cooperative games (or among criteria in bi-capacities ). Lastly, we give the expression of the Banzhaf interaction index in terms of each of the bipolar Möbius transform and bipolar co-Möbius transform as it was done for a cooperative game.