Sequential bankruptcy problems

In this paper, we analyze sequential bankruptcy problems, which generalize bankruptcy problems. They contain the problems of sharing water in a transboundary river and of allocating expedition rewards in projects. We provide three mechanisms for generalizing rules for bankruptcy problems to rules for sequential bankruptcy problems: the upwards, the downwards, and the two-steps mechanisms. Further, we characterize the upwards constrained equal awards, the upwards constrained equal losses, and the upwards proportional rules on the basis of upwards composition and upwards path independence. Moreover, we compare the three mechanisms based on inheritance of well-established properties for bankruptcy rules to the setting of sequential bankruptcy rules.