Kokovin, Sergey and Nahata, Babu and Zhelobodko, Evgeny (2010): All solution graphs in multidimensional screening. Forthcoming in: Journal of New Economic Association, Russia
Download (353kB) | Preview
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|
|Original Title:||All solution graphs in multidimensional screening|
|English Title:||All solution graphs in multidimensional screening|
|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
|Depositing User:||Sergey Kokovin|
|Date Deposited:||04. Apr 2011 07:01|
|Last Modified:||29. Apr 2015 17:39|
Andersson, T., 2005. "Profit maximizing nonlinear pricing." Economic letters 88, 135-139.
Andersson, T., 2008. "Efficiency properties of nonlinear pricing schedules without the single-crossing condition," Economic letters 99(2), 364-66.
Armstrong, M., Rochet, J-C., 1999. "Multi-dimensional Screening:" A User's Guide, European Economic Review 43, 959-79.
Armstrong, M., 2006. "Recent Developments in the Economics of Price Discrimination," in: Blundell, Newey, and Persson, (Eds), Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress of the Econometric Society, Volume II, 97-141, Cambridge: Cambridge University Press.
Brito, D.L., Hamilton, J.H., Slutsky, J.E., and Stiglitz, J., 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, 42, 61--77.
Guesnerie, R., Seade, J., 1982. "Nonlinear Pricing in a Finite Economy," Journal of Public Economics 17, 157-179.
Harary, F. and E.M. Palmer., 1973. "Graphical Enumeration}," Academic press, New York and London.
Kokovin, S., Nahata, B., and Zhelobodko, E., 2010. "Multidimensional screening under nonlinear costs: Limits of standard approach," Economic letters, forthcoming.
Nahata, B., Kokovin, S., and Zhelobodko, E., 2002. "Package Sizes, Tariffs, Quantity Discount and Premium," http://econpapers.repec.org/paper/wpawuwpgt/0307002.htm.
Rochet, J.-C., 1987. "A Necessary and Sufficient Condition for Rationalizability in a Quasi-linear Context," Journal of Mathematical Economics, 16(2), 191-200.
Rochet, J.-C., Stole, L., 2003. "The Economics of Multidimensional Screening," Advances in Economics and Econometrics: Theory and Applications: Eighth World Congress Vol I. (Eds.) Mathias Dewatripont, Lars Peter Hansen and Stephen J. Turnovsky. Cambridge: Cambridge University Press.
Rochet, J.-C., Chone, P. (1998). "Ironing, Sweeping and Multi-dimensional Screening," Econometrica , 66(4), 174-93.
Rockafellar, R.T., 1993. "Lagrange Multipliers and Optimality," SIAM Review v.35, No.2
Stole, L.A. 2007. "Price Discrimination and Competition" in: Handbook of Industrial Organization, 2007 (first edition), v. 3, edts. M.Armstrong, R.H.Porter, Elsevier, Amsterdam, London, pp.2221-2299.
Wilson, R., 1993. "Nonlinear Pricing}," Oxford University Press, Oxford, UK.
Vohra, R.V., 2008 "Paths, Cycles and Mechanism Design," mimeo, Kellogg School of Business.