Manipulation via merging and splitting in claims problems

Abstract

In claims problems, we study coalitional manipulations via claims merging and splitting. We characterize (division) rules that are non-manipulable via (pairwise) splitting and that also satisfy standard axioms of equal treatment of equals, consistency, and continuity. And we obtain a similar result for non-manipulability via (pairwise) merging. Copyright Springer-Verlag Berlin/Heidelberg 2003Claims problem, non-manipulability via pairwise splitting , non-manipulability via pairwise merging ,

Inequality preserving rationing

“…Our result therefore relates to earlier results characterizing the proportional method by non-manipulability in Moulin (1987) and Chun (1988) who consider arbitrary reallocations, and to de Frutos (1999) and Ju (2003) who consider manipulation by merging and splitting of claims resulting in a variable number of agents.…”

A monotonic and merge-proof rule in minimum cost spanning tree situations

“…In a context where the agents consume arbitrary quantities of possibly different goods, Sprumont (2005) characterizes the Aumann-Shapley cost sharing method, used to distribute the total generated cost that ensures that agents never find it profitable to split or to merge their consumptions. O'Neill (1982), Chun (1988), De Frutos (1999, Moulin (2002), Ju (2003), and Ju et al (2007) study split and merge-proofness in claim and bankruptcy problems. Moulin (2007Moulin ( , 2008) also studies split and merge-proofness in the context of job scheduling.…”

Merging and splitting in cooperative games: some (im)possibility results

“…9 In the context of bankruptcy problems there exists large classes of allocation rules that are merging-proof or splitting-proof respectively (Ju 2003). …”

“…The rule that for any convex game selects this allocation was introduced independently by Fujishige (1980) and Dutta and Ray (1989). Suppose that  is a strictly concave function on R. For bankruptcy problems, the constrained equal awards bankruptcy rule is merging-proof (de Frutos 1999, Ju 2003). As pointed out in Thomson (2003), the allocation chosen by the constrained equal awards rule corresponds to the payoff vector chosen by the Fujishige-Dutta-Ray rule for the associated bankruptcy game.…”