Discrete Screening

Alejandro Francetich and Burkhard C. Schipper
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Burkhard C. Schipper: Department of Economics, University of California Davis

No 375, Working Papers from University of California, Davis, Department of Economics

Abstract: We consider a principal who wishes to screen an agent with \emph{discrete} types by offering a menu of \emph{discrete} quantities and \emph{discrete} transfers. We assume that the principal's valuation is discrete strictly concave and use a discrete first-order approach. We model the agent's cost types as non-integer, with integer types as a limit case. Our modeling of cost types allows us to replicate the typical constraint-simplification results and thus to emulate the well-treaded steps of screening under a continuum of contracts. We show that the solutions to the discrete F.O.C.s need not be unique \textit{even under discrete strict concavity}, but we also show that there cannot be more than two optimal contract quantities for each type, and that---if there are two---they must be adjacent. Moreover, we can only ensure weak monotonicity of the quantities \textit{even if virtual costs are strictly monotone}, unless we limit the ``degree of concavity'' of the principal's utility. Our discrete screening approach facilitates the use of rationalizability to solve the screening problem. We introduce a rationalizability notion featuring robustness with respect to an open set of beliefs over types called \textit{$\Delta$-O Rationalizability}, and show that the set of $\Delta$-O rationalizable menus coincides with the set of usual optimal contracts---possibly augmented to include irrelevant contracts.

Keywords: Screening; discrete concave optimization; rationalizability; level-$k$ reasoning (search for similar items in EconPapers)
JEL-codes: D82 (search for similar items in EconPapers)
Pages: 27
Date: 2025-10-23
New Economics Papers: this item is included in nep-cta, nep-des and nep-mic
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