A COMPUTATIONAL APPROACH TO THE COINCIDENCE OF EGALITARIAN SOLUTIONS FOR COST-SHARING GAMES

The pre-nucleolus is a popular egalitarian solution concept for cost-sharing games. A drawback of this concept is that an associated cost allocation often cannot be calculated in polynomial time. Therefore, it would be convenient to know whether the pre-nucleolus of a particular game coincides with the outcome of a cost-allocation method which is computationally less demanding. We provide operational conditions for a coincidence of the pre-nucleolus (point) of a cost-sharing game and the center of the game's imputation set (CIS vector). These conditions can be checked with little computational effort as compared to the potential savings in terms of computation time of a general solution algorithm.