We identify and characterize a natural and intuitive class of mechanisms called the k-pivotal mechanisms. The axioms used are efficiency, pairwise strategyproofness, equal treatment of equals and weak linearity. We also identify the subclass of these mechanisms which do not run a budget deficit...

Assuming a ‘spectrum’ or ordering of the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally...