Solution Structures in Non-Ordered Discrete Screening Problems : Trees, Stars and Cycles

We analyze discrete-type self-selection problem when valuations are multidimensional or non-ordered, and costs can be non-separable. Spence-Mirrlees condition is generalized for these situations to reveal solution structures like trees, quot;bushesquot; and quot;starsquot;. Pareto efficient quot;starquot; structures are shown to be non-degenerate, as well as cycles. Cycles can result in overall inefficiency and non-implementability of solutions. Under costs separability or alternative assumptions, optimal solutions are free of quot;essentialquot; cycles which make them implementable with small rewards. Non-trivial counter-examples show that our assumptions are essential