Market Design

• One-to-one matching of discrete agents to discrete units or other agents.
• One-to-many matching of discrete agents to discrete units or other agents. 
• Matching of the above kind with finitely many available match types.
• Assignment of discrete agents to objects when the objects are owned by other agents. 
• One-to-one (bilateral trade) or one-to-many (auctions) matching of an indivisible object to discrete agents in the presence of transfers and probabilistic information structures about the preferences of agents.

The student should be able to:

• Explain the relationship between Game Theory and Market Design.
• Define a social choice rule and its role in economic theory. 
• Explain the definition of and the use of the concept of the game form.
• Describe some applications of each model in the real world.
• Describe matching theory and its application to school assignment, labor markets, and organ transplantation.
• Describe auction theory and its applications to trade. 
• Describe the major general results of the theory and their implications. 

                    The “Rural Hospitals” Theorem.

                    The lattice structure of the core.

                    Revenue equivalence principle.

                    Revelation principle.

The student should be able to:

• Find a stable matching in a two-sided, one to one market.
• Find a core allocation of indivisible goods to agents with unit-demand.
• Find the core of a matching market when there are multiple terms of trade.
• Find an extremal stable matching in a two-sided, one-to-many market.
• Demonstrate the manipulability of core-extremal matching rules by one side of the market.
• Calculate the optimal bidding strategies in common auction forms. 
• Calculate the top-trading-cycles algorithm, and its generalization when there are waiting lists.
• Calculate Myerson’s optimal mechanism for auctions with independent private values.
• Calculate Vickrey-Clarke-Groves payment schemes for auction problems

The student should be able to:

• Independently suggest the application of one of the models taught in class when confronted with a relevant real-world problem.
• Identify the weaknesses of the various algorithms taught. In particular, compare and contrast deferred acceptance with top-trading-cycles.
• Identify novel applications of the theory, along with any deficits in the theory preventing it from being immediately applied here. 

• Roth, Alvin. 2015. Who Gets What–and Why : The New Economics of Matchmaking and Market Design. Boston: Houghton Mifflin Harcourt.
• Hart, Sergiu. 1992. “Games in Extensive and Strategic Forms.” Handbook of Game Theory with Economic Applications 1: 19–40.
• Moulin, Hervé. 1994. “Social Choice.” Handbook of Game Theory with Economic Applications 2: 1091–1125.
• Thomson, William. 2001. “On the Axiomatic Method and Its Recent Applications to Game Theory and Resource Allocation.” Social Choice and Welfare 18 (2): 327–86. https://doi.org/10.1007/s003550100106.
• ———. 2002. “The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics.” Econometrica 70 (4): 1341–78. https://doi.org/10.1111/1468-0262.00335.
• Roth, Alvin E., and Marilda Sotomayor. 1992. “Two-Sided Matching.” Handbook of Game Theory with Economic Applications 1: 485–541.
• Sönmez, Tayfun, and M. Utku Ünver. 2011. “Matching, Allocation, and Exchange of Discrete Resources.” In Handbook of Social Economics, 1:781–852. Elsevier.
• Milgrom, Paul. Putting auction theory to work. Cambridge University Press, 2004. Chapters 1 through 3.

• Abdulkadiroğlu, Atila, and Tayfun Sönmez. 2003. “School Choice: A Mechanism Design Approach.” The American Economic Review 93 (3): 729–47. 
• Alcalde, José, and Salvador Barberà. 1994. “Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems.” Economic Theory 4 (3): 417–35. https://doi.org/10.1007/BF01215380.
• Baïou, Mourad, and Michel Balinski. 2007. “Characterizations of the Optimal Stable Allocation Mechanism.” Operations Research Letters 35 (3): 392–402. https://doi.org/10.1016/j.orl.2006.06.004.
• Becker, Gary S., and Julio Jorge Elias. 2007. “Introducing Incentives in the Market for Live and Cadaveric Organ Donations.” The Journal of Economic Perspectives 21 (3): 3–24.
• Demange, Gabrielle, David Gale, and Marilda Sotomayor. 1986. “Multi-Item Auctions.” Journal of Political Economy 94 (4): 863–72.
• Gul, Faruk, and Ennio Stacchetti. 1999. “Walrasian Equilibrium with Gross Substitutes.” Journal of Economic Theory 87 (1): 95–124. https://doi.org/10.1006/jeth.1999.2531.
• ———. 2000. “The English Auction with Differentiated Commodities.” Journal of Economic Theory 92 (1): 66–95. https://doi.org/10.1006/jeth.1999.2580.
• Kara, Tarik, and Tayfun Sönmez. 1996. “Nash Implementation of Matching Rules.” Journal of Economic Theory 68 (2): 425–39. https://doi.org/10.1006/jeth.1996.0024.
• Krishna, Vijay. 2010. Auction Theory. Burlington, MA: Academic Press/Elsevier. (Selections only)
• Roth, Alvin E. 1982. “The Economics of Matching: Stability and Incentives.” Mathematics of Operations Research 7 (4): 617–28. https://doi.org/10.1287/moor.7.4.617.
• Roth, Alvin E. 1982. “Incentive Compatibility in a Market with Indivisible Goods.” Economics Letters 9 (2): 127–32. https://doi.org/10.1016/0165-1765(82)90003-9.
• Shapley, Lloyd, and Herbert Scarf. 1974. “On Cores and Indivisibility.” Journal of Mathematical Economics 1 (1): 23–37. https://doi.org/10.1016/0304-4068(74)90033-0.
• Sönmez, Tayfun. 1994. “Strategy-Proofness in Many-to-One Matching Problems.” Economic Design 1 (1): 365–80. https://doi.org/10.1007/BF02716633.
• Tarik, and Tayfun Sönmez. 1996. “Nash Implementation of Matching Rules.” Journal of Economic Theory 68 (2): 425–39. https://doi.org/10.1006/jeth.1996.0024.