Resource allocation with partial responsibilities for initial endowments

This paper studies a resource allocation problem in which each individual is responsible but in general only partially for his initial endowment. We consider pure-exchange economies with initial endowments but we do not assume the individual rationality axiom, taking the society to consist of citizens who cannot opt out of it. We characterize a class of allocation rules which are parametrized by income redistribution codes. In particular, we characterize a one-parameter family of income redistribution codes, in which one extreme corresponds to the case where everybody is 100% responsible for his initial endowment and the other extreme corresponds to the case where nobody is responsible for his endowment at all