Sharing sequentially triggered losses (revised)

When losses caused by one agent onto another triggers losses to a third, "victim" turns into "injurer" in the chain's subsequent steps. Should agents be responsible for the direct loss they cause or also bear some of the indirect losses they trigger? Through an axiomatic approach, we characterize the fixed-fraction rules, holding each agent accountable for a fraction of the direct harm she causes while the chain's initiator is liable for the residual. We also examine contested individual losses. Extending on the well-known principle of equalizing losses, we show that losses can be distributed equidistant to the agents' ideal allocations.