{"ID":2851345,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.20921","arxiv_id":"2510.20921","title":"Discrete Screening","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{$Δ$-O Rationalizability}, and show that the set of $Δ$-O rationalizable menus coincides with the set of usual optimal contracts -- possibly augmented to include irrelevant contracts.","short_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,...","url_abs":"https://arxiv.org/abs/2510.20921","url_pdf":"https://arxiv.org/pdf/2510.20921v1","authors":"[\"Alejandro Francetich\",\"Burkhard C. Schipper\"]","published":"2025-10-23T18:19:46Z","proceeding":"econ.TH","tasks":"[\"econ.TH\",\"cs.GT\"]","methods":"[]","has_code":false}