Rakesh Vohra
Rakesh Vohra

MANAGERIAL ECONOMICS & DECISION SCIENCES
Visiting Professor of Managerial Economics & Decision Sciences

Print Overview

Rakesh V. Vohra is a Visiting Professor of Managerial Economics and Decision Sciences from the University of Pennsylvania. Professor Vohra is a leading global expert in mechanism design, an innovative area of game theory that brings together economics, engineering and computer science. His economics research in mechanism design focuses on the best ways to allocate scarce resources when the information required to make the allocation is dispersed and privately held, an increasingly common condition in present-day environments. His work has been critical to the development of game, auction and pricing theory — for example, the keyword auctions central to online search engines — and spans such areas as operations research, market systems and optimal pricing mechanisms.

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, 2006-2013
John L. and Helen Kellogg Professor of Managerial Economics and Decision Science, Kellogg School of Management, Northwestern University, 1999-2013
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

Grants and Awards
Executive MBA Program Outstanding Teaching Awards, Kellogg School of Management, 2012
EMP-86 (Core)
Sidney J. Levy Teaching Award, Kellogg School of Management, 2007-2008
Economic Theory Fellow, Society for the Advancement of Economic Theory, one year

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
Schummer, James and Rakesh Vohra. 2013. Assignment of Landing Slots. American Economic Journal: Microeconomics. 5(2): 164-185.
Vohra, Rakesh, Shankar Balakrishnan and J.C. Gomez. 2011. The Tempered Aspirations Solution for Bargaining Problems with a Reference Point. Mathematical Social Sciences. 62(3): 144-150.
Gómez, Juan Camilo, Sundar Balakrishnan and Rakesh Vohra. 2011. The Tempered Aspirations solution for bargaining problems with a reference point. Mathematical Social Sciences. 62(2): 144-150.
Bikhchandani, Sushil, Sven de Vries, James Schummer and Rakesh Vohra. 2011. An Ascending Vickrey Auction for Selling Bases of a Matroid. Operations Research. 59(2): 400-413.
Vohra, Rakesh, Randall Berry and Michael Honig. 2010. Spectrum Markets: Motivation, Challenges, and Implications. IEEE Communications Magazine. 48(11): 146-155.
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.
de Vries, Sven, James Schummer and Rakesh Vohra. 2007. On Ascending Vickrey Auctions for Heterogeneous Objects. Journal of Economic Theory. 132(1): 95-118.
Beigman, Eyal and Rakesh Vohra. 2006. Learning from Revealed Preference. Proceedings of the 2006 ACM Conference of Electronic Commerce. 7: 36-42.
Sethuraman, Jay, Chung Piaw Teo and Rakesh Vohra. 2006. Anonymous Monotonic Social Welfare Functions. Journal of Economic Theory. 128(1): 232-254.
Smorodinsky, Rann, Rakesh Vohra and Alvaro Sandroni. 2003. Calibration with Many Checking Rules. Mathematics of Operations Research. 28(1): 141-153.
Sethuraman, Jay, Chung Piaw Teo and Rakesh Vohra. 2003. Integer Programming and Arrowian Social Welfare Functions. Mathematics of Operations Research. 28(2): 309-326.
de Vries, Sven and Rakesh Vohra. 2003. Combinatorial Auctions: A Survey. INFORMS Journal on Computing. 15(3): 289-304.
Baliga, Sandeep and Rakesh Vohra. 2003. Market Research and Market Design. BE Journals in Theoretical Economics. 3(1)
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.
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.
Solan, Eilon and Rakesh Vohra. 2001. Correlated Equilibrium and Quitting Games. Mathematics of Operations Research. 26(3): 601-610.
Vohra, Rakesh. 1999. Analysis of LP relaxations for multiway and multicut problems. Networks. 34(2): 102-114.
Vohra, Rakesh. 1999. The Replacement Principle and Tree Structured Preferences. Economics Letters. 63(2): 175-180.
Foster, Dean P. and Rakesh Vohra. 1999. Regret in the On-line Decision Problem. Games and Economic Behavior. 29(1-2): 7-35.
Vohra, Rakesh. 1999. New Randomized Rounding Algorithms. Operations Research Letters. 24(3): 105-114.
Foster, Dean P. and Rakesh Vohra. 1998. An Axiomatic Characterization of a Class of Locations In Trees. Operations Research. 46(3): 345-354.
Foster, Dean P. and Rakesh Vohra. 1998. Asymptotic Calibration. Biometrika. 85(2): 379-390.
Vohra, Rakesh. 1998. Rounding Algorithms for Covering Problems. Mathematical Programming. 80(1): 63-90.
Foster, Dean P. and Rakesh Vohra. 1997. Calibrated Learning and Correlated Equilibrium. Games and Economic Behavior. 21(1-2): 40-55.
Vohra, Rakesh. 1996. A Parametric Worst Case Analysis for a Machine Scheduling Problem. Operations Research. 45(1): 116-125.
Vohra, Rakesh. 1996. An Axiomatic Characterization of Some Locations In Trees. European Journal of Operational Research. 90(1): 78-84.
Vohra, Rakesh. 1995. New Algorithms for an Ancient Scheduling Problem. Journal of Computer and System Science. 51(3): 359-366.
Vohra, Rakesh. 1994. Average Case Analysis of a Heuristic for the Assignment Problem. Mathematics of Operations Research. 19(3): 513-522.
Vohra, Rakesh and Nicholas G. Hall. 1993. A Probabilistic Analysis of the Maximal Covering Location Problem. Discrete Applied Mathematics. 43(2): 175-183.
Hall, Nicholas G. and Rakesh Vohra. 1993. Towards Equitable Distribution via Proportional Equity Constraints. Mathematical Programming. 58(2): 287-294.
Hall, Nicholas G. and Rakesh Vohra. 1993. Pareto Optimality and a Class of Set Covering Heuristics. Annals of Operations Research. 43(5): 279-284.
Vohra, Rakesh and Dean P. Foster. 1993. A Randomized Rule for Selecting Forecasts. Operations Research. 41(4): 704-709.
Foster, Dean P. and Rakesh Vohra. 1992. An Economic Argument for Affirmative Action. Research and Society. 4(2): 176-188.
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.
Vohra, Rakesh. 1990. Computing the Bandwidth of Interval Graphs. SIAM J on Discrete Mathematics. 3(3): 373-375.
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.
Vohra, Rakesh. 1989. Distance Weighed Voting and a Single Facility Location Problem. European Journal of Operational Research. 41(3): 314-320.
Vohra, Rakesh. 1989. Finding the Most Vital Arcs in a Network. Operations Research Letters. 8(2): 73-76.
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. 1988. A Quick Heuristic for some Cyclic Staffing Problems with Breaks. Journal of the Operational Research Society. 39(11): 1057-1061.
Vohra, Rakesh. 1988. Probabilistic Analysis of the Longest Hamiltonian Tour Problem. Networks. 18(1): 13-18.
Vohra, Rakesh. 1988. A Simple Trade-Off Model for Maximal and Multiple Coverage. Geographical Analysis. 20(30): 220-230.
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 Cost of Consecutivity in the (5,7) Cyclic Staffing Problem. IIE Transactions. 19(3): 13-18.
Vohra, Rakesh. 1987. The Orienteering Problem. Naval Research Logistics. 34(307-318)
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.
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.
Jain, Kamal and Rakesh Vohra. Forthcoming. On Stability of the Core. International Journal of Game Theory.
de Castro, Luciano and Rakesh Vohra. 2013. A Unifying Goal for Energy Policy: Improving Economic Efficiency.
de Castro, Luciano and Rakesh Vohra. 2013. On the Design of Electricity Markets.
de Castro, Luciano, Pedro N. Ferreira and Rakesh Vohra. 2013. The Re-Regulation Debate: Average vs. Marginal Pricing.
Schummer, James and Rakesh Vohra. 2012. Voting with Money.
Vohra, Rakesh and Mallesh M. Pai. 2012. Auction Design with Fairness Concerns: Subsidies vs. Set-Aside.
Vohra, Rakesh and Itai Sher. 2011. Price Discrimination Through Communication.
Nazarzadeh, Hamid, Amin Saberi and Rakesh Vohra. 2007. Dynamic Cost Per Action Mechanisms and Applications to On-line Advertising.
Malakhov, Alexey and Rakesh Vohra. 2006. Optimal Auctions for Asymmetrically Budget Constrained Bidders.
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.
Gómez, Juan Camilo, Sundar Balakrishnan and Rakesh Vohra. Bargaining problems with arbitrary reference points.
Book Chapters
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.
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.
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.
Books
Vohra, Rakesh and Lakshman Krishnamurthi. 2012. Principles of Pricing: An Analytical Approach. Cambridge, UK: Cambridge University Press.
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.
Conference Proceedings
Vohra, Rakesh, T. Ngyuen, H. Zhou, Randall Berry and Michael Honig. 2011. "The Price of Free Spectrum to Heterogeneous Users.".
Vohra, Rakesh, H. Zhou, Randall Berry and Michael Honig. 2011. "Spectrum Markets with Interference Complementarities.".
Vohra, Rakesh, Randall Berry, Michael Honig, H. Zhou and T. Ngyuen. 2011. "The Impact of Additional Unlicensed Spectrum on Wireless Services Competition.".

 
Print Teaching
Teaching Interests
Pricing strategies, economics and optimization
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)
Managerial Economics introduces the economic principles of pricing. It provides an overview of methods to estimate sensitivity of buyers to price, the trade-off between margin and volume, price discrimination and pricing in competitive environments.

Full-Time / Part-Time MBA
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.