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Rakesh Vohra
Rakesh Vohra

MANAGERIAL ECONOMICS & DECISION SCIENCES
John L. and Helen Kellogg Professor of Managerial Economics & Decision Sciences
Director of the Center for Mathematical Studies in Economics & Management

Print Overview
Rakesh V. Vohra is the John K. and Helen Kellogg Professor of Managerial Economics and Decision Sciences. He is also Director of the Center for Mathematical Studies in Economics and Management Science. He has published widely in game theory and operations research. His area of expertise is auction theory and pricing. In addition he serves on a number of editorial boards and is co-editor of the International Journal of Game Theory.


Area of Expertise

Pricing Strategies
Print Vita
Education
PhD, 1985, Mathematics, University of Maryland
MS, 1981, Operational Research, London School of Economics
BS, 1980, Mathematics, University College London, Honors

Academic Positions
Professor (by courtesy), Robert R. McCormick School of Engineering and Applied Science, Northwestern University, 2006-present
John L. and Helen Kellogg Professor of Managerial Economics and Decision Science, Kellogg School of Management, Northwestern University, 1999-present
Visiting Researcher, Microsoft Research, 2006-2006
Visiting Professor, Indian School for Business, 2006-2006
Visiting Scholar, California Institute of Technology, 2005-2005
Visiting Professor, Indian School for Business, 2004-2004
METEOR Fellow, University of Maastricht, 2003-2003
Cycle and Carriage Visiting Professor, College of Business, National University of Singapore, 2000-2000
Professor of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 1998-1999
Visiting Associate Professor, Kellogg School of Management, Northwestern University, 1997-1998
Associate Professor of Management Science of Industrial Engineering, Fisher College of Business, Ohio State University, 1991-1998
Visiting Associate Professor, Sloan School of Management, Massachusetts Institute of Technology, 1992-1993
Assistant Professor of Management Science, Fisher College of Business, Ohio State University, 1985-1991
Visiting Assistant Professor, Graduate School of Business, University of Chicago, 1991-1991
Visiting Scholar, Southern Methodist University, 1989-1989
Visiting Member, Institute for Mathematics and its Applications, University of Minnesota, 1987-1988

Editorial Positions
Associate Editor, Games and Economic Behavior, 2005-Present
Co-Editor, International Journal of Game Theory, 2008-Present
Associate Editor, Mathematics of Operations Research, 2005-Present
Associate Editor, International Journal of Game Theory, 2001-2008
Associate Editor, Management Science, 1995-2005
Associate Editor, Operations Research, 2003-2005

 
Print Research
Research Interests
Pricing strategies, auctions and game theory

Articles
de Vries, Sven, James Schummer and Rakesh Vohra. 2007. On Ascending Vickrey Auctions for Heterogeneous Objects. Journal of Economic Theory. 132(1): 95-118.
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de Vries, Sven, Marc E. Posner and Rakesh Vohra. 2007. Polyhedral Properties of the K-median Problem on a Tree. Mathematical Programming. 110(2): 261-285.
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Sethuraman, Jay, Chung Piaw Teo and Rakesh Vohra. 2006. Anonymous Monotonic Social Welfare Functions. Journal of Economic Theory. 128(1): 232-254.
Beigman, Eyal and Rakesh Vohra. 2006. Learning from Revealed Preference. Proceedings of the 2006 ACM Conference of Electronic Commerce. 7: 36-42.
Abstract
Moulin, Herve and Rakesh Vohra. 2003. Characterization of additive cost sharing methods. Economics Letters. 80(3): 399-407.
Schummer, James and Rakesh Vohra. 2003. Auctions for Procuring Options. Operations Research. 51(1): 41-51.
Abstract
Smorodinsky, Rann, Rakesh Vohra and Alvaro Sandroni. 2003. Calibration with Many Checking Rules. Mathematics of Operations Research. 28(1): 141-153.
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de Vries, Sven and Rakesh Vohra. 2003. Combinatorial Auctions: A Survey. INFORMS Journal on Computing. 15(3): 289-304.
Sethuraman, Jay, Chung Piaw Teo and Rakesh Vohra. 2003. Integer Programming and Arrowian Social Welfare Functions. Mathematics of Operations Research. 28(2): 309-326.
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Baliga, Sandeep and Rakesh Vohra. 2003. Market Research and Market Design. BE Journals in Theoretical Economics. 3(1)
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Solan, Eilon and Rakesh Vohra. 2002. Correlated Equilibrium Payoffs and Public Signalling in Absorbing Games. International Journal of Game Theory. 31(1): 91-121.
Schummer, James and Rakesh Vohra. 2002. Strategy-Proof Location on a Network. Journal of Economic Theory. 104(2): 405-428.
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Solan, Eilon and Rakesh Vohra. 2001. Correlated Equilibrium and Quitting Games. Mathematics of Operations Research. 26(3): 601-610.
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Vohra, Rakesh. 1999. Analysis of LP relaxations for multiway and multicut problems. Networks. 34(2): 102-114.
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Vohra, Rakesh. 1999. New Randomized Rounding Algorithms. Operations Research Letters. 24(3): 105-114.
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Foster, Dean P. and Rakesh Vohra. 1999. Regret in the On-line Decision Problem. Games and Economic Behavior. 29(1-2): 7-35.
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Vohra, Rakesh. 1999. The Replacement Principle and Tree Structured Preferences. Economics Letters. 63(2): 175-180.
Foster, Dean P. and Rakesh Vohra. 1998. An Axiomatic Characterization of a Class of Locations In Trees. Operations Research. 46(3): 345-354.
Abstract
Foster, Dean P. and Rakesh Vohra. 1998. Asymptotic Calibration. Biometrika. 85(2): 379-390.
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Vohra, Rakesh. 1998. Rounding Algorithms for Covering Problems. Mathematical Programming. 80(1): 63-90.
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Foster, Dean P. and Rakesh Vohra. 1997. Calibrated Learning and Correlated Equilibrium. Games and Economic Behavior. 21(1-2): 40-55.
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Vohra, Rakesh. 1996. A Parametric Worst Case Analysis for a Machine Scheduling Problem. Operations Research. 45(1): 116-125.
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Vohra, Rakesh. 1996. An Axiomatic Characterization of Some Locations In Trees. European Journal of Operational Research. 90(1): 78-84.
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Vohra, Rakesh. 1995. New Algorithms for an Ancient Scheduling Problem. Journal of Computer and System Science. 51(3): 359-366.
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Vohra, Rakesh. 1994. Average Case Analysis of a Heuristic for the Assignment Problem. Mathematics of Operations Research. 19(3): 513-522.
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Vohra, Rakesh and Nicholas G. Hall. 1993. A Probabilistic Analysis of the Maximal Covering Location Problem. Discrete Applied Mathematics. 43(2): 175-183.
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Vohra, Rakesh and Dean P. Foster. 1993. A Randomized Rule for Selecting Forecasts. Operations Research. 41(4): 704-709.
Abstract
Hall, Nicholas G. and Rakesh Vohra. 1993. Pareto Optimality and a Class of Set Covering Heuristics. Annals of Operations Research. 43(5): 279-284.
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Hall, Nicholas G. and Rakesh Vohra. 1993. Towards Equitable Distribution via Proportional Equity Constraints. Mathematical Programming. 58(2): 287-294.
Vohra, Rakesh and Dean P. Foster. 1992. A Probabilistic Analysis of the K-Location Problem. American Journal of Mathematical and Management Sciences. 12(1): 75-87.
Foster, Dean P. and Rakesh Vohra. 1992. An Economic Argument for Affirmative Action. Research and Society. 4(2): 176-188.
Abstract
Vohra, Rakesh. 1990. Computing the Bandwidth of Interval Graphs. SIAM J on Discrete Mathematics. 3(3): 373-375.
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Hall, Nicholas G. and Rakesh Vohra. 1989. Absolute Bounds on Optimal Cost for a Class of Set Covering Problems. Zeitschrift fur OR. 33: 181-192.
Vohra, Rakesh. 1989. Distance Weighed Voting and a Single Facility Location Problem. European Journal of Operational Research. 41(3): 314-320.
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Vohra, Rakesh. 1989. Finding the Most Vital Arcs in a Network. Operations Research Letters. 8(2): 73-76.
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Foster, Dean P. and Rakesh Vohra. 1989. Probabilistic Analysis of a Heuristic for the Dual Bin Packing Problem. Information Processing Letters. 31(6): 287-290.
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Vohra, Rakesh. 1988. A Quick Heuristic for some Cyclic Staffing Problems with Breaks. Journal of the Operational Research Society. 39(11): 1057-1061.
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Vohra, Rakesh. 1988. A Simple Trade-Off Model for Maximal and Multiple Coverage. Geographical Analysis. 20(30): 220-230.
Vohra, Rakesh. 1988. Probabilistic Analysis of the Longest Hamiltonian Tour Problem. Networks. 18(1): 13-18.
Abstract
Vohra, Rakesh. 1987. The Cost of Consecutivity in the (5,7) Cyclic Staffing Problem. IIE Transactions. 19(3): 13-18.
Vohra, Rakesh and Nicholas G. Hall. 1987. The On-Line Assignment Problem with Random Effectiveness and Costly Information. Oerations Research Letters. 6(4): 163-168.
Vohra, Rakesh. 1987. The Orienteering Problem. Naval Research Logistics. 34(307-318)
Abstract
Vohra, Rakesh. 1984. Counting Spanning Trees in a Graph of Kleitman and Golden and its Generalization. Journal of the Franklin Institute. 318(5): 349-355.
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Working Papers
Bae, Junjik, Eyal Beigman, Randall Berry, Michael Honig and Rakesh Vohra. Forthcoming. Bounds on the Inefficiency of Sequential Auctions. IEEE Journal on Selected Areas in Communications.
Abstract
Jain, Kamal and Rakesh Vohra. Forthcoming. On Stability of the Core. International Journal of Game Theory.
Abstract
Schummer, James and Rakesh Vohra. 2009. Assignment of Landing Slots.
Schummer, James and Rakesh Vohra. 2009. Voting with Money.
Bikhchandani, Sushil, Sven de Vries, James Schummer and Rakesh Vohra. 2008. An Ascending Vickrey Auction for Selling Bases of a Matroid.
AbstractLink
Nazarzadeh, Hamid, Amin Saberi and Rakesh Vohra. 2007. Dynamic Cost Per Action Mechanisms and Applications to On-line Advertising.
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Malakhov, Alexey and Rakesh Vohra. 2006. Optimal Auctions for Asymmetrically Budget Constrained Bidders.
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Malakhov, Alexey and Rakesh Vohra. 2004. Single and Multi-Dimensional Optimal Auctions- A Network Approach.
Teo, Chung Piaw and Rakesh Vohra. 2003. Negative Cycles and Afriat's Theorem.
Book Chapters
Vohra, Rakesh and Lakshman Krishnamurthi. "Principles of Pricing: An Analytical Approach.." Cambridge, England: Cambridge University Press.
Schummer, James and Rakesh Vohra. 2007. "Mechanism Design without Money." In Algorithmic Game Theory, edited by Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani, 243-266. Cambridge, UK: Cambridge University Press.
Abstract
Lahaie, Sebastien, David Pennock, Amin Saberi and Rakesh Vohra. 2007. "Sponsored Search Auctions." In Algorithmic Game Theory, edited by Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani, 699-716. Cambridge, UK: Cambridge University Press.
Vohra, Rakesh. 2006. "The Ubiquitous Farkas Lemma." In Perspectives in Operations Research: Papers in Honor of Saul Gass' 80th Birthday, edited by Frank B. Alt, Michael C. Fu, Bruce L. Golden, 199-210. New York, NY: Springer Science+Business Media.
de Vries, Sven and Rakesh Vohra. 2004. "Design of Combinatorial Auctions." In Handbook of Quantitative Supply Chain Analysis: Modeling in the E-business Era, edited by David Simchi-Levi, S. David Wu and Zuo-Jun Shen, 247-292. Kluwer.
Bikhchandani, Sushil, Sven de Vries, James Schummer and Rakesh Vohra. 2002. "Linear Programming and Vickrey Auctions." In Mathematics of the Internet: E-auction and Markets, edited by B. Dietrich and R. Vohra, 75-116. New York: Springer-Verlag.
AbstractLink
Books
Vohra, Rakesh. 2005. Advanced Mathematical Economics. London, UK: Routledge.
Vohra, Rakesh. 2002. Mathematics of the Internet. Springer-Verlag.
Vohra, Rakesh. Paths, Cycles and Mechanism Design.
Abstract

 
Print Teaching
Teaching Interests
Pricing strategies, economics and optimization
Full-Time / Part-Time MBA
Decision Making Under Uncertainty (DECS-433-0)

This course counts toward the following majors: Decision Sciences.

Provides frameworks for reasoning about decisions in uncertain environments. Case studies and experiments are used to motivate the importance of probabilistic reasoning to avoid the systematic biases that cloud managers' decision making. Formal probabilistic tools are introduced and their relevance to modern business issues is conveyed via cases, exercises, and class experiments. Some of the applications include: inventory management with uncertain demand, principal-agent models, herd behavior, selection bias, rare events, real options and risk. The course is self-contained, and should be of value to all students, including those with prior exposure to formal probability models.

Statistical Methods For Management Decisions (DECS-434-0)

This course counts toward the following majors: Decision Sciences.

This sequel to DECS-433 extends the statistical techniques learned in that course to allow for the exploration of relationships between variables. Topics include one- and two-population hypothesis testing, correlation, simple and multiple regression analysis, and qualitative variables. The course also covers applications of the material and a number of case studies. Extensive use of spreadsheet statistical analysis software is required.

Turbo Decision Making and Statistics (DECS-445-0)
coming soon

Pricing Strategies (MECN-446-0)

This course counts toward the following majors: Decision Sciences, Entrepreneurship & Innovation, Managerial Analytics, Managerial Economics.

This course provides students with a comprehensive framework for formulating and implementing pricing strategies. Techniques that take account of the often imprecise and uncertain information to which management has access are useded to analyze the influence of costs, demand and competition on the pricing decision. Also discussed are research methods that can complement managerial judgment and the importance of maintaining consistency with other elements of the marketing mix. Special attention is devoted to the design of pricing schemes that segment the market, such as peak-load pricing, product bundling and nonlinear pricing. The course also studies vertical pricing problems (transfer pricing, pricing and distribution), legal constraints on pricing and industrial pricing (bidding). Actual pricing schemes in various industries and selected cases are used for illustrative and analytical purposes.

Executive MBA
Statistical Decision Analysis (DECSX-434-0)
Statistical Decision Analysis explores the use of sample data for estimating,predicting, forecasting and making business decisions.

Managerial Economics (MECNX-430-0)