Multidimensional mechanism design: Finite-dimensional approximations and efficient computation
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2010-07-01
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Abstract
Multidimensional mechanism design problems have proven difficult to solve by extending techniques from the onedimensional case. This paper considers mechanism design problems with multidimensional types when the seller's cost function is not separable across buyers. By adapting results obtained by Border [Border, K. 1991. Implementation of reduced form auctions: A geometric approach. Econometrica 59 1175-1187], we transform the seller's problem into a representation that only involves "interim" variables and eliminates the dimensionality dependence on the number of buyers. We show that the associated infinite-dimensional optimization problem posed by the theoretical model can be approximated arbitrarily well by a sequence of finite-dimensional linear programming problems. We provide an efficient-i.e., terminating in polynomial time in the problem size-method to compute the separation oracle associated with the Border constraints and incentive compatibility constraints. This implies that our finite-dimensional approximation is solvable in polynomial time. Finally, we illustrate how the numerical solutions of the finite-dimensional approximations can provide insights into the nature of optimal solutions to the infinite-dimensional problem in particular cases. ©2010 INFORMS.
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Belloni, A, G Lopomo and S Wang (2010). Multidimensional mechanism design: Finite-dimensional approximations and efficient computation. Operations Research, 58(4 PART 2). pp. 1079–1089. 10.1287/opre.1100.0824 Retrieved from https://hdl.handle.net/10161/4439.
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Alexandre Belloni
Alexandre Belloni is a Professor of Decision Sciences at the Fuqua School of Business at Duke University. He received his Ph.D. in Operations Research from the Massachusetts Institute of Technology (2006) and a M.Sc. in Mathematical Economics from IMPA (2002). He deferred the offer to join the faculty at Duke University to accept the IBM Herman Goldstein Postdoctoral Fellowship (2006-2007).
Professor Belloni’s research interests are on statistics and optimization and on their applications to Economics and Business. His current research focuses on developing and analyzing methods for model selection in Econometric problems, and for solving Mechanism Design problems. He became 2014-2016 F.M. Kirby Research Fellow, and received the 2007 Young Researchers Competition in Continuous Optimization Award and the second prize at the INFORMS 2006 George Nicholson Student Paper Award.
His research papers have appeared in journals such as Econometrica, Review of Economic Studies, Annals of Statistics, Marketing Science, Management Science and Operations Research. He has received a grant from the National Science Foundation and has held visiting appointments in other prestigious institutes. He has consulted with the electrical energy industry in Brazil. His recent teaching has been the an elective Daytime MBA on Data Analytics, the core Daytime MBA Statistics course and the Weekend MBA Statistics course.
Giuseppe Lopomo
Giuseppe (Pino) Lopomo is the Alan D. Schwartz Distinguished Professor of Business Administrations at the Fuqua School of Business, Duke University. He also has a courtesy appointment at the Economics Department of Duke University.
He has a Laurea Magna cum laude from Bocconi University in Milan, Italy, and a Ph.D. in Business Administration from the Stanford Graduate School of Business.
Before joining the faculty at Duke, he was Assistant Professor of Economics at the Stern School of Business of New York University, and visited the Economics department of the University of Michigan for one year.
Currently, Professor Lopomo teaches Managerial Economics and Competitive Analysis to MBA students. He has taught courses on similar topics to undergraduate and PhD students.
Professor Lopomo's research focuses on applied game theory, auction and mechanism design. His work has been published in leading journals of economics including The Review of Economic Studies, International Economic Review, Journal of Economic Theory, Games and Economic Behavior, The Rand Journal of Economics and American Economic Journal: Microeconomics
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