Proportionality in Bargaining Games: status quo-Proportional Solution and Consistency

The status quo-proportional solution for bargaining games is studied. The consistency of the solution is proved, and it is used to give an axiomatic characterization of this solution. The logarithmic transformation of player's utilities is considered and is used to establish the relation between some bargaining solutions: the Nash bargaining solution, the egalitarian, the utilitarian and the status quo-proportional solutions.