On obligation rules for minimum cost spanning tree problems

Tijs et al. (2006) introduce the family of obligation rules in minimum cost spanning tree problems. We prove that obligation rules are closely related with the marginalistic values of the irreducible game. We also provide axiomatic characterizations of obligation rules with two basic monotonicity properties, namely population monotonicity (if new agents join a "society", no agent from the "initial society" can be worse off) and strong cost monotonicity (if a number of connection costs increase, no agent can be better off). In this class, the folk rule is the only allocation rule satisfying equal treatment of equals.