ECON 703 Syllabus: Fall, 2025

Official Matters

Course Material

Grading

There will be 2 or 3 ungraded problem sets for  the course.

Section 0101: Mondays/Wednesdays 2:00 pm - 3:15 pm, Tydings 1101

Texts

Office Hours

Topics (Approximately One Week for Each)

1. Games and Equilibria

• Games in Strategic Form.
• Best Response Correspondences
• Nash Equilibria -- Nash's Theorem, Debreu, van Glicksburg, Fan. Tarski
FT (Chapter 1)
Debreu, G., Theory of Value, Wiley. 1959.
Vives, X., Oligopoly Pricing: Old Ideas and New Tools, MIT Press. 2001.
http://econweb.umd.edu/~vincent/econ703/MTLec1.pdf


2. Dynamic Games, Equivalence and Equilibria

• Extensive Form Games -- Definition.
• Nodes, Information Sets, Actions, Payoffs.
• Behavior Strategies, Mixed Strategies, Perfect Recall, Kuhn's Theorem.
• Games of Perfect Information, Backward Induction
• Games of Imperfect Information, Subgame Perfect Equilibria
FT (Chapter 3)
Elmes, S. and P. Reny, "On the strategic equivalence of extensive form games", Journal of Economic Theory, 64, pp.1-23 1994
Kuhn, H., "Extensive Games and the Problem of Information," Annals of Mathematics Studies, 28, 1953.
Reny, P., "Rationality in Extensive Form Games", Journal of Economic Perspectives ,6(4), pp.103-118,1992
Shaked, A. and J. Sutton, "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Game", Econometrica, 52, pp.1351-1364, 1984
Rubinstein, A., "Perfect Equilibrium in a Bargaining Model", Econometrica, 50, pp. 97-110, 1982,
Rubinstein, A. and M. Piccione, "One the Interpretation of Decision Problems with Imperfect Recall", Games and Economic Behavior, 20, pp. 3-24, 1997,
Selten, R., "The Chain-Store Paradox,"  Theory and Decision, 9, 1978.
Selten, R., "Reexamination of the Perfectness Concept for Equilibrium Points of Extensive Form Games,"  International Journal of Game Theory, 4, 1975.
Thompson, F., "Equivalence of Games in Extensive Form,"; Rand Corporation, RN59, 1952.
http://econweb.umd.edu/~vincent/econ703/MTLec2.pdf


3. Refinements of Nash Equilibria

• Perfect and Proper Equilibrium
• Sequential Equilibrium
• Perfect Bayesian Equilibrium
• Stable Sets
• Signalling games and further refinements
FT (Chapter 8)
Cho, I-K, and D. Kreps, "Signalling Games and Stable Equilibria"  Quarterly Journal of Economics, 102, 1987.
Fudenberg, D. and J.Tirole "Perfect Bayesian Equilibria and Sequential Equilibria"  Journal of Economic Theory, 53,1991.
Kohlberg, E. and J.-F,Mertens, "On the Strategic Stability of Equilibria,"  Econometrica, 54, 1986.
Kreps, D. and R. Wilson, "Sequential Equilibria,"  Econometrica, 540 , 1982.
Selten, R., "A Reexamination of the Perfectness Concept for Equilibrium Points of Extensive Form Games,"  International Journal of Game Theory, 4, 1975.
http://econweb.umd.edu/~vincent/econ703/MTLec3.pdf


4. Games of Incomplete Information, Bayesian Nash Equilibrium

• Bayesian Games, Bayesian Nash Equilibria.
• The Revelation Principle.
• Harsanyi and Myerson
FT (Chapter 6)
Athey, S. "Single-crossing properties ....", Econometrica , 2001.
Harsanyi, J., "Games of Incomplete Information Played by Bayesian Players,"   Management Science, 14 , 1967-68.
Milgrom, P. and C.Shannon, "Monotone comparative statics", Econometrica , 1994.
MacAdams, D., "Isotone equilibrium in games....", Econometrica , 2003.
Reny, "On the existence of monotone pure-strategy equilibria in Bayesian games", Econometrica, 2011.
http://econweb.umd.edu/~vincent/econ703/MTLec4.pdf


5. Implementation: The Mechanism Design Approach
   

• Myerson and Incentive Compatibility in One-Dimension.
FT (Chapter 7)
Myerson, R.,"Mechanism Design by an Informed Principle,"   Econometrica, 51(6), 1983.
http://econweb.umd.edu/~vincent/econ703/MTLec5.pdf


6. Applications of Mechanism Design

• Optimal Bargaining.
• Auctions and the Revenue Equivalence Theorem.
• Bilateral Trade.
• Regulation of a Monopolist.
FT (Chapter 7)
Baron, D. and R. Myerson,"Regulating a Monopolist with Unknown Costs,"   Econometrica, , 50(4) 1982.
Myerson, R.,"Incentive Compatibility and the Bargaining Problem,"   Econometrica, 1979.
Myerson, R.,"Optimal Auction Design,"   Mathematics of Operations Research, 6 ,1981.
Myerson, R., and M. Satterthwaite, "Efficient Mechanisms for Bilateral Trade,"   Journal of Economic Theory, 29, 1983.
http://econweb.umd.edu/~vincent/econ703/MTLec6.pdf


7. Multi-Dimensional Mechanism Design

• Multi-Dimensional Incentive Compatibility -- Rochet.
• Manelli - Vincent, DDT.
Aliprantis, C. and K.Border,K, Infinite Dimensional Analysis: A Hitchhikers Guide. Springer , 1999}
Armstrong, M.,"Multi-Product Non-liner Pricing,"   Econometrica, 64(1), 1996.
Daskalakis, C.,Deckelbaun, A. and C. Tzamos,"Strong Duality for a Multiple-Good Monopolist"   Econometrica, 85(3) ,2017.
Edwards,C.H. Jr., Advanced Calculus of Several Variables, Dover Publications, 1994.
Luenberger, D., Optimization by Vector Space Methods, New York: John Wiley & Sons, 1969.
ManelliA. and A. Kleiner.,"Strong Duality and Monopoly Pricing,"   Econometrica, 2019.
Manelli A. and D. Vincent.,"Bundling as an Optimal Mechanism for a Multi-Good Monopolist,"   Journal of Economic Theory, 46(2),2006.
Manelli A. and D. Vincent.,"Multi-Dimensional Mechanism Design, Revenue Maximization and the Multi-Good Monopolist,"   Journal of EconomicTheory, 46(2),2007.
McAfee, R. P. and J. McMillan.,"Multi-Dimensional Incentive Compatibility and Mechanism Design,"   Journal of Economic Theory, 46(2), 1988.
Rochet, J.-C.,"The Taxation Principle and Multi-time Hamilton-Jacobi Equations,"  Journal of Mathematical Economics, 14(2),1985.
Rockafellar, R.T., Convex Analysis, Princeton: Princeton University Press, 1970.
http://econweb.umd.edu/~vincent/econ703/MTLec7.pdf


8. Imperfect Competition, Bundling and Differentiated Products

• Discrete Choice Models of Product Differentiation.
• Aggregation and Existence Theorems.
• Multi-product Firms: Multi-nomial Nested Logit; Two-Product Firms and Mixed Bundling.
• Pure Bundling and Competition.
Armstrong, Mark and John Vickers, "Competitive Nonlinear Pricing and Bundling", Review of Economic Studies (2010).
Caplin, Andrew and Barry Nalebuff, "Aggregation and Imperfect Competition:
On the existence of equilibrium",  Econometrica  (1991).
Gans, J. and S. King, "Paying For Loyalty: Product Bundling in Oligopoly",  Journal of Industrial Economics, (2006).
Matutes, Carmen and Pierre Regibeau,""Mix and Match": Product Compatibility without Network Externalities", Rand Journal of Economics,  (1988).
Vincent, Daniel, "Mixed Bundling and Mergers", Review of Network Economics (2024).
Zhou, J., "Competitive Bundling",  Econometrica  (2017).
http://econweb.umd.edu/~vincent/econ703/MTLec10.pdf


9. Dominant Strategy Implementation

• One Dimension:Manelli-Vincent, Gershkov, et. al..
• Multi-dimensions.
Border, K., "Implementation of reduced form auctions: A geometric approach," Econometrica, 59(4), 1991, pp.1175-1187.
Cremer, J. and R. McLean, "Full extraction of the surplus in Bayesian and dominant strategy auctions", Econometrica,56, pp.1247-1257, 1988.
d'Aspremont, C., and L. A. Gerard-Varet,"Incentives and incomplete information", Journal of Public Economics, 11, pp.25-45}1979,
Gershkov A., Goeree, J., Kushnir, A., B. Moldovanu and X. Shi, "On the equivalence of Bayesian and dominant strategy implementation," Econometrica, 18, 2013, pp. 197-220.
Manelli, A., and D. Vincent, "Bayesian and dominant-strategy implementation in the independent private-values model," Econometrica 137, 2010, pp. 153-185
Manelli, A., and D. Vincent, "Dominant-strategy and Bayesian Incentive Compatibility in the Multi-Object Trading Environment," Journal of Mathematical Economics, 82, pp. 214-226, 2019.
Matthews, S., "On the implementability of reduced form auctions," Econometrica 52, 1984, pp. 1519-1522.
Williams, S., "A characterization of efficient, Bayesian incentive compatible mechanisms," Economic Theory 14, 1999, pp. 155-180.
http://econweb.umd.edu/~vincent/econ703/MTLec8.pd


10. Majorization and Optimization
    

• Majorization as a Partial Order.
• Extreme Points of Sets of Majorized Functions.
• Fan-Lorentz and Optimization
• Applications.
Border, K., "Implementation of reduced form auctions: A geometric approach," Econometrica, 59(4), 1991, pp.1175-1187.
Bergeman, D., T. Heumann, S. Morris,C. Sorokin, E. Winter, "Optimal Information Disclosure In Classic Auctions", AER: Insights, 4(3),  pp. 371-388, 2022.
Gershkov A., Goeree, J., Kushnir, A., B. Moldovanu and X. Shi, "On the equivalence of Bayesian and dominant strategy implementation," Econometrica, 18, 2013, pp. 197-220.
Kleiner, A., B. Moldovanu and P. Stark, "Extreme Points and Majorization: Economic Applications," Econometrica 89(4), 2021, pp. 1557-1593
Manelli, A., and D. Vincent, "Bayesian and dominant-strategy implementation in the independent private-values model" Econometrica, 137, pp. 153-185, 2010.
Matthews, S., "On the implementability of reduced form auctions," Econometrica 52, 1984, pp. 1519-1522.
Yang, K.H. and A. Zentefis, "Monotone Function Intervals: Theory and Applications," American Economic Review 114(8), 2024, pp. 2239-2270.
http://econweb.umd.edu/~vincent/econ703/MTLec9.pd


11. Comparison of Information Structures
1. Blackwell Experiments
2. Weaker Orders: Monotone Decision Problems
3. Stronger Orders: ``Reveal and Refine''.
1. Athey, S. and J. Levin (2018): “The Value of Information in Monotone Decision Problems,” Re-
   search in Economics, 72(1), pp. 101-116.
2. Blackwell, D. (1953): “Equivalent Comparisons of Experiments,” Annals of Mathematical Statistics,
   24(2), pp. 265-272.
3. Brooks, B., A. Frankel, E. Kemenica (2024): “Comparison of Signals,” American Economic Review, 114 (9), pp. 2981-3006.
4. Green, J., N. Stokey (2022): “Two Representations of Information Structures and their Compar-
   isons,” Decisions in Economics and Finance, 45, pp. 541-547.
   Karlin, S. and H. Rubin (1956): “The Theory of Decision Procedures With Monotone Likelihood
   Ratio Distributions,” Annals of Mathematical Statistics, 27, pp. 272-279.
   Lehman, E. (1988): “Comparing Location Experiments,” Annals of Statistics, 16(2), pp. 521-533.
5. http://econweb.umd.edu/~vincent/econ703/MTLec12.pdf

12. Nash Bargaining:Nash in Nash Approach

• Nash Bargaining and the `Nash Program'.
• Nash-in-Nash Bargaining and Multi-lateral Negotiations.
Collard-Wexler, Alan, Gowrisankaran, G., and R. Lee., "Nash-in-Nash Bargaining: A Micro-foundation for Applied Work", Journal of Political Economy (2019).
Crawford, G. and A. Yurucoglu, "The Welfare Effects of Bundling in Multi-channel Television Markets", American Economic Review, 102(2) (2012), pp. 643-685.
Horn, H. and A. Wolinsky,"Bilateral Monopolies and Incentives for Mergers", Rand Journal of Economics, 19(3) (1988): 408-419.
McAfee, P. and M. Schwartz, "Opportunism in Multi-lateral Vertical Contracting", American Economic Review 84(1), (1994): 210-230.
Nash, J., "The Bargaining Problem", Econometrica 18(2), (1950), pp. 155-162.
Vincent, Daniel R., "Multilateral Negotiations and Opportunism", working paper, 2022.
Whinston, M.,11Lectures in Anti-trust Theory., (2006),: Chapter 4.
http://econweb.umd.edu/~vincent/econ703/MTLec11.pdf


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