The monoclus of a coalitional game

The analysis of single-valued solution concepts, providing payoffs to players for the grand coalition only, has a long tradition. Opposed to most of this literature we analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce several closely related allocation scheme rules, each resulting in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game with transferable utilities has a PMAS. Monotonicities, which measure the payoff difference for a player between two nested coalitions, are the driving force. These monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Variants are obtained by considering different domains and/or different collections of monotonicities. We deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues.