Abstract
It is known that no additive division rules exist for bankruptcy problems. In this paper, we study a restricted additivity property which we call “feasible set additivity” (FSA). This property requires division rules to be additive when the set of feasible allocation vectors for a sum of problems does not include allocations that were unfeasible when considering each problem separately.In addition, we characterize the random arrival rule as the only division rule satisfying FSA and equal treatment of equals for two and three-agent cases. We also show that this characterization holds when the endowment is small enough in relation to the claims, while the question of whether it holds in general remains open.
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