Kimmo Berg
ABSTRACT
Optimal screening has been studied in economics, game theory, and recently computer science. We study the problem in a nonlinear pricing application, where a monopoly designs a price schedule from which the buyers self-select the quality they wish to consume. We formulate a multidimensional model with buyers' utility functions that need not satisfy the standard single-crossing assumption. We characterize the solution with the first-order optimality conditions and present a framework for analyzing the solution. With the framework, the structure of the solution is easily illustrated and the sensitivity analysis can be done. We give numerical examples that demonstrate the properties of the solution. With these observations, we discuss the complexity of the problem and solving the problem under limited information. We examine what information the monopoly needs when adjusting the price schedule to increase the profit. This paper applies, e.g., to pricing situations in electronic commerce where the seller may have limited information available, and the seller learns about the buyers' preferences online when doing the business.
- M. Armstrong. Multiproduct nonlinear pricing. Econometrica, 64:51--75, 1996.Google Scholar
Cross Ref
- M. Armstrong and J.-C. Rochet. Multi-dimensional screening: A user's guide. European Economic Review, 43:959--979, 1999.Google ScholarCross Ref
- R. Aron, A. Sundararajan, and S. Viswanathan. Intelligent agents in electronic markets for information goods: customization, preference revelation and pricing. Decision Support Systems, 51:764--786, 2006. Google ScholarDigital Library
- S. Basov. Multidimensional Screening. Springer, Heidelberg, 2005.Google Scholar
- K. Berg and H. Ehtamo. Learning in optimal screening problem when utility functions are unknown. Submitted manuscript. URL: http://www.sal.hut.fi/Publications/pdf-files/mber07.pdf, Nov. 2007.Google Scholar
- D. P. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, MA, second edition, 2004.Google Scholar
- P. Bolton and M. Dewatripont. Contract Theory. MIT Press, Cambridge, MA, 2005.Google Scholar
- C. H. Brooks, R. S. Gazzale, R. Das, J. O. Kephart, J. K. Mackie-Mason, and E. H. Durfee. Model selection in an information economy: Choosing what to learn. Computational Intelligence, 18:566--582, 2002.Google ScholarCross Ref
- V. Conitzer and T. Sandholm. Complexity of mechanism design. In Proceedings of the 18th Annual Conference on Uncertainty in Artificial Intelligence (UAI-02), pages 103--111, San Francisco, CA, 2002. Morgan Kaufmann. Google ScholarDigital Library
- R. K. Dash, N. R. Jennings, and D. C. Parkes. Computational-mechanism design: A call to arms. IEEE Intelligent Systems: Special Issue on Agents and Markets, 18:40--47, 2003. Google ScholarDigital Library
- H. Ehtamo, K. Berg, and M. Kitti. An adjustment scheme for nonlinear pricing problem with two buyers. European Journal of Operational Research. Forthcoming. URL: http://www.sal.hut.fi/Publications/pdf-files/meht06.pdf, Dec. 2008.Google Scholar
- J. Feigenbaum, M. Schapira, and S. Shenker. Distributed Algorithmic Mechanism Design, pages 363--384. Algorithmic Game Theory. Cambridge University Press, 2007.Google ScholarCross Ref
- D. Fudenberg and D. K. Levine. The theory of learning in games. MIT press, 1999.Google Scholar
- D. Fudenberg and J. Tirole. Game Theory. MIT Press, Cambridge, 1991.Google Scholar
- R. P. McAfee and J. McMillan. Multidimensional incentive compatibility and mechanism design. Journal of Economic Theory, 46:335--354, 1988.Google ScholarCross Ref
- M. Mussa and S. Rosen. Monopoly and product quality. Journal of Economic Theory, 18:301--317, 1978.Google ScholarCross Ref
- B. Nahata, S. Kokovin, and E. Zhelobodko. Self-selection under non-ordered valuations: type-splitting, envy-cycles, rationing and efficiency. Working paper, 2001.Google Scholar
- B. Nahata, S. Kokovin, and E. Zhelobodko. Solution structures in non-ordered discrete screening problems: Trees, stars and cycles. Working paper, July 2004.Google Scholar
- B. Nahata, S. Kokovin, and E. Zhelobodko. Efficiency, over and underprovision in package pricing: How to diagnose? Working paper, Mar. 2006.Google Scholar
- N. Nisan and A. Ronen. Algorithmic mechanism design. Games and Economic Behavior, 35:166--196, 2001.Google ScholarCross Ref
- D. C. Parkes. Online Mechanisms, pages 411--442. Algorithmic Game Theory. Cambridge University Press, 2007. Google ScholarDigital Library
- J.-C. Rochet and P. Chone. Ironing, sweeping, and multidimensional screening. Econometrica, 66:783--826, 1998.Google ScholarCross Ref
- J.-C. Rochet and L. A. Stole. The economics of multidimensional screening, volume 1 of Advances in Economics and Econometrics, pages 150--197. Cambridge University Press, 2003.Google Scholar
- T. Sandholm. Automated mechanism design: A new application area for search algorithms. In International Conference on Principles and Practice of Constraint Programming (CP-03), 2003.Google ScholarDigital Library
- T. Sandholm. Perspectives on multiagent learning. Artificial Intelligence, 171:382--391, 2007. Google ScholarDigital Library
- M. Spence. Multi-product quantity-dependent prices and profitability constraints. The Review of Economics Studies, 47:821--841, 1980.Google ScholarCross Ref
- G. Weiss. Multiagent systems: A modern approach to distributed artificial intelligence. MIT Press, Cambridge, MA, 1999. Google ScholarDigital Library
- R. B. Wilson. Nonlinear pricing. Oxford University Press, 1993.Google Scholar
Index Terms
- Multidimensional screening: online computation and limited information
Recommendations
Multi-dimensional mechanism design with limited information
EC '12: Proceedings of the 13th ACM Conference on Electronic CommerceWe analyze a nonlinear pricing model with limited information. Each buyer can purchase a large variety, d, of goods. His preference for each good is represented by a scalar and his preference over d goods is represented by a d-dimensional vector. The ...
Costly Multidimensional Screening
EC '22: Proceedings of the 23rd ACM Conference on Economics and ComputationA screening instrument is costly if it is socially wasteful andproductive otherwise. A principal screens an agent with multidimensional private information and quasilinear preferences that are additively separable across two components: a one-...
Correcting vindictive bidding behaviors in sponsored search auctions
In this study, we aim to develop a pricing mechanism that reduces the effects resulted by vindictive advertisers who bid on sponsored search auctions run by search engine providers. In particular, we aim to ensure payment fairness and price stability in ...
Comments