SELF-SELECTION UNDER NON-ORDERED VALUATIONS: TYPE-SPLITTING, ENVY-CYCLES, RATIONING AND EFFICIENCY

We analyze self-selection problem when valuations are non-ordered. The corresponding package-pricing solution has specific graph structure. It is helpful in deriving weak su±cient conditions for both partial e±ciency and Pareto-e±ciency. Unlike the ordered valuations case, Pareto e±ciency is shown to be a non-pathological case. Pareto e±ciency and positive consumer surplus are mutually exclusive. Under costs separability optimal package-pricing scheme is shown implementable by small rewards. Counter-examples show that our assumptions are essential. In certain non-ordered situations, package-optimization setting with rations is more appropriate than the standard setting.