All solution graphs in multidimensional screening

Kokovin, Sergey and Nahata, Babu and Zhelobodko, Evgeny (2010): All solution graphs in multidimensional screening. Forthcoming in: Journal of New Economic Association, Russia

Abstract

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.

• Item Type: MPRA Paper
• Language: English
• Keywords: incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs
• Subjects: L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L11 - Production, Pricing, and Market Structure ; Size Distribution of Firms; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L10 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L12 - Monopoly ; Monopolization Strategies; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D42 - Monopoly

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