Pseudo-Banzhaf Values in Bicooperative Games

In conventional cooperative games, it is assumed that each player will choose whether he/she joins a coalition or not. In bicooperative games defined by Bilbao, each player is allowed to choose one among three alternatives such as to be a defender, to be a fence-sitter and to be a defeater. In this paper, we define a solution which is the probabilistic value of a player when coalitions not containing him/her are equally likely to arise for a bicooperative game. We call this solution the pseudo-Banzhaf value on the class of bicooperative games. Axiomatizations to show rationality of the solution are given. Further, we formulate a weighted majority game as a bicooperative game and give a numerical example