The proportional rule for problems with constraints and claims.
The paper studies a problem of resource distribution among different agents who have claims on it when there are some constraints in the problem (the problem with constraints and claims). This kind of problem generalizes, for instance, the bankruptcy problems and PERT problems. The paper shows how the principle of `proportionality' can be defined for problems with constraints and claims. Two rules based on this principle are presented: the proportional rule (which satisfies weak Pareto optimality) and the extended proportional rule (which satisfies Pareto optimality). It is checked which of the desirable properties of the allocation rule are satisfied by the rules proposed in the paper. It is found that the relations among the properties in the new model are completely different from the ones of their counterparts in bankruptcy problems (e.g., even though, in bankruptcy problems, Pareto optimality is compatible with additivity, composition up, and linearity, in the new model Pareto optimality becomes incompatible with any of these properties). All the rules satisfying non-manipulability are characterized. It is shown that the extended proportional rule is the only rule satisfying Pareto optimality, consistency, non-manipulability, and the lower bound requirement over subsets. Some open questions are posed.
scientific article; zbMATH DE number 1891783