A coalitional extension of the ordinal Shapley-Shubik value

In cooperative game theory it is known that two-person bargaining problems have no relevant ordinal solution. For three-player bargaining problems, Shapley and Shubik propose an ordinal rule. However, this rule does not take into account the worth of proper subcoalitions of size 2. In this paper, we fill this gap by proposing a generalization of the Shapley-Shubik rule for non transferable utility games. The resulting solutions, when applied to transferable utility games, always belong to the core, which makes it a relevant alternative to other core-selectors such as the nucleolus. We also apply the new solution to a practical case related to mining and natural resources management.