Reducing incentive constraints in bidimensional screening

Calagua, Braulio (2018): Reducing incentive constraints in bidimensional screening.

Abstract

This paper studies screening problems with quasilinear preferences, where agents' private information is two-dimensional and the allocation instrument is one-dimensional. A pre-order in the set of types is defined comparing types by their marginal valuation for the instrument, which allows reducing the incentive compatibility constraints that must be checked. With this approach, the discretized problem becomes computationally tractable. As an application, it is numerically solved an example from Lewis and Sappington [Lewis, T. and Sappington, D. E., 1988. Regulating a monopolist with unknown demand and cost functions. The RAND Journal of Economics, 438-457].

• Item Type: MPRA Paper
• Language: English
• Keywords: two-dimensional screening; Spence-Mirrlees condition; incentive compatibility; regulation of a monopoly.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; L - Industrial Organization > L5 - Regulation and Industrial Policy > L51 - Economics of Regulation

References

Araujo, A., Vieira, S., and Calagua, B. (2019). A necessary optimality condition in two-dimensional screening. Working Paper.

Armstrong, M. (1996). Multiproduct nonlinear pricing. Econometrica: Journal of the Econometric Society, pages 51–75.

Armstrong, M. (1999). Optimal regulation with unknown demand and cost functions. Journal of Economic Theory, 84(2):196–215.

Barelli, P., Basov, S., Bugarin, M., and King, I. (2014). On the optimality of exclusion in multi-dimensional screening. Journal of Mathematical Economics, 54:74–83.

Baron, D. P. and Myerson, R. B. (1982). Regulating a monopolist with unknown costs. Econometrica: Journal of the Econometric Society, pages 911–930.

Basov, S. (2001). Hamiltonian approach to multi-dimensional screening. Journal of Mathematical Economics, 36(1):77–94.

Belloni, A., Lopomo, G., and Wang, S. (2010). Multidimensional mechanism design: Finite-dimensional approximations and efficient computation. Operations Research, 58(4-part-2):1079–1089.

Berg, K. and Ehtamo, H. (2009). Learning in nonlinear pricing with unknown utility functions. Annals of Operations Research, 172(1):375.

Evans, L. (1998). Partial Differential Equations, volume 19 of Graduate studies in mathematics. American Mathematical Society.

Judd, K., Ma, D., Saunders, M. A., and Su, C.-L. (2018). Optimal income taxation with multidimensional taxpayer types. Working Paper.

Laffont, J.-J. and Martimort, D. (2001). The theory of incentives: the principal-agent model. Princeton university press.

Laffont, J.-J., Maskin, E., and Rochet, J.-C. (1987). Optimal nonlinear pricing with two-dimensional characteristics. Information, Incentives and Economic Mechanisms, pages 256–266.

Lewis, T. R. and Sappington, D. E. (1988a). Regulating a monopolist with unknown demand. The American Economic Review, pages 986–998.

Lewis, T. R. and Sappington, D. E. (1988b). Regulating a monopolist with unknown demand and cost functions. The RAND Journal of Economics, pages 438–457.

McAfee, R. P. and McMillan, J. (1988). Multidimensional incentive compatibility and mechanism design. Journal of Economic theory, 46(2):335–354.

Mussa, M. and Rosen, S. (1978). Monopoly and product quality. Journal of Economic theory, 18(2):301–317. Myerson, R. B. (1979). Incentive compatibility and the bargaining problem. Econometrica: Journal of the Econometric Society, pages 61–73.

Rochet, J.-C. (2009). Monopoly regulation without the Spence–Mirrlees assumption. Journal of Mathematical Economics, 45(9-10):693–700.

Tarkiainen, R. and Tuomala, M. (1999). Optimal nonlinear income taxation with a two-dimensional population; a computational approach. Computational Economics, 13(1):1–16.

Wilson, R. (1996). Nonlinear pricing and mechanism design. Handbook of computational economics, 1:253–293.