Characterizations of Proportional Rules in Claims Problems

When resources are divided among agents, resources are in many cases divided proportionally to their claims. In this paper, we provide new axiomatizations of generalized proportional rules based on the axiom “decentralizability” due to Moulin [13,14,15]. Decentralizability requires that no reallocation by any coalition can affect the awards of the agents outside the coalition. Our results can explain the results of Chun [7] and Ju=Miyagawa=Sakai [10] based on non-manipulability requirements as corollaries. We moreover introduce a coalitional form game called a “claims reallocation game” which describes a claims problem under any established division rule. We require the core of a claims reallocation game be always nonempty for claimants to make an agreement on how to divide. We show that under a certain condition, the core of a claims reallocation game is always nonempty if and only if the division rule is a generalized proportional rule. JEL Classification: C71, D63, D70.