Rationing a commodity along fixed paths

A commodity is divided among agents with single-peaked preferences. The commodity is either infinitely divisible or comes in indivisible units. Arationing methodelicits individual peaks (demands); if the commodity is overdemanded (resp. underdemanded), no agent receives more (resp. less) than his peak. Afixed-pathrationing method allocates an overdemanded “good” along a path independent of individual demands, except that an agent receives exactly his demand if it is below the path-generated share. An underdemanded “bad” is allocated similarly alonganotherpath. The four properties efficiency, strategyproofness, resource monotonicity, and consistency characterize the set of fixed path rationing methods