Complexity of solution structures in nonlinear pricing
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This paper characterizes and enumerates the possible solution structures in nonlinear pricing problem when the number of buyer types is given. It is shown that the single-crossing property, which is a standard assumption in the literature, reduces the complexity of solving the problem dramatically. The number of possible solution structures is important when the pricing problem is solved under limited information.
KeywordsNonlinear pricing Screening Complexity Combinatorics Single-crossing condition Graph theory
The author is grateful to Mirko Ruokokoski and Arttu Klemettilä for the helpful comments and suggestions. The author would like to thank the two anonymous reviewers for their valuable suggestions and corrections.
- Araujo, A., & Moreira, H. (1999). Adverse selection problems without the single crossing condition. Econometric Society World Congress 2000 Contributed Papers 1874. Google Scholar
- Basov, S. (2005). Multidimensional screening. Heidelberg: Springer. Google Scholar
- Berg, K., & Ehtamo, H. (2008). Multidimensional screening: online computation and limited information. In ACM international conference proceeding series: Vol. 42. ICEC 2008: proceedings of the 10th international conference on electronic commerce, Austria: Innsbruck. Google Scholar
- Bertsekas, D. (1999). Nonlinear programming. Belmont: Athena Scientific. Google Scholar
- Brito, D. L., Hamilton, J. H., Slutsky, S. M., & Stiglitz, J. E. (1990). Pareto efficient tax structures. Oxford Economic Papers, 42, 61–77. Google Scholar
- Conitzer, V., & Sandholm, T. (2002). Complexity of mechanism design. In Proceedings of the 18th annual conference on uncertainty in artificial intelligence (UAI-02) (pp. 103–111). Google Scholar
- Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge: MIT Press. Google Scholar
- Kokovin, S., Nahata, B., & Zhelobodko, E. (2011). All solution graphs in multidimensional screening (Working paper). Google Scholar
- Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. New York: Oxford University Press. Google Scholar
- Nahata, B., Kokovin, S., & Zhelobodko, E. (2001). Self-selection under non-ordered valuations: type-splitting, envy-cycles, rationing and efficiency (Working paper). Department of Economics, University of Louisville. Google Scholar
- Nahata, B., Kokovin, S., & Zhelobodko, E. (2004). Solution structures in non-ordered discrete screening problems: trees, stars and cycles (Working paper). Department of Economics, University of Louisville. Google Scholar
- Nahata, B., Kokovin, S., & Zhelobodko, E. (2006). Efficiency, over and underprovisioning in package pricing: how to diagnose? (Working paper). Department of Economics, University of Louisville. Google Scholar
- Sloane, N. J. A. (2008). The on-line encyclopedia of integer sequences. http://www.research.att.com/~njas/sequences/.
- Wilson, R. B. (1995). Nonlinear pricing and mechanism design. In H. Amman, D. Kendrick, & J. Rust (Eds.), Handbook of computational economics (Vol. 1, pp. 249–289). Amsterdam: Elsevier. Google Scholar
- Wilson, R. (1993). Nonlinear pricing. London: Oxford University Press. Google Scholar