Le, Phuong (2013): Competitive Equilibrium in the Random Assignment Problem.
This is the latest version of this item.
Preview 
PDF
MPRA_paper_66624.pdf Download (178kB)  Preview 
Abstract
This paper studies the problem of random assignment with fractional endowments. Fractional endowments complicate matters because the assignment has to make an agent weakly better off than his endowment. I first formulate an exchange economy that resembles the random assignment problem and prove the existence of competitive equilibrium in this economy. I then propose a pseudomarket mechanism for the random assignment problem that is based on the competitive equilibrium. This mechanism is individually rational, Pareto Optimal and justified envyfree but not incentive compatible.
Item Type:  MPRA Paper 

Original Title:  Competitive Equilibrium in the Random Assignment Problem 
Language:  English 
Keywords:  Random Assignment, Competitive Equilibrium, Mechanism Design 
Subjects:  D  Microeconomics > D4  Market Structure, Pricing, and Design > D47  Market Design D  Microeconomics > D5  General Equilibrium and Disequilibrium > D50  General 
Item ID:  66624 
Depositing User:  Phuong Le 
Date Deposited:  15 Sep 2015 06:56 
Last Modified:  29 Sep 2019 04:40 
References:  Abdulkadiroglu, A., Che, Y.K., and Yasuda, Y. (2011). Resolving conflicting preferences in school choice: The "boston mechanism" reconsidered. American Economic Review, 101(1):399410. Abdulkadiroglu, A., Che, Y.K., and Yasuda, Y. (2015). Expanding ``choice'' in school choice. American Economic Journal: Microeconomics, 7(1):142. Abdulkadiroglu, A. and Sonmez, T. (1999). House allocation with existing tenants. Journal of Economic Theory, 88(2):233260. Abdulkadiroglu, A. and Sonmez, T. (2003). School choice: A mechanism design approach. The American Economic Review, 93(3):729747. Athanassoglou, S. and Sethuraman, J. (2010). House allocation with fractional endowments. International Journal of Game Theory, pages 133. Birkhoff, G. (1946). Tres observaciones sobre el algebra lineal. Univ. Nac Tucuman Rev. Ser., 5:147151. Bogomolnaia, A. and Moulin, H. (2001). A new solution to the random assignment problem. Journal of Economic Theory, 100:295328. Budish, E., Che, Y.K., Kojima, F., and Milgrom, P. (2013). Designing random allocation mechanisms: Theory and applications. American Economic Review, 103(2):585623. Erdil, A. and Ergin, H. (2008). What's the matter with tiebreaking? improving efficiency in school choice.The American Economic Review, 98(3):669689. Gale, D. and Shapley, L.~S. (1962). College admissions and the stability of marriage. American mathematical monthly, pages 915. Hylland, A. and Zeckhauser, R. (1979). The efficient allocation of individuals to positions. Journal of Political Economy, 87(2):293314. MasColell, A. (1992). Equilibrium theory with possibly satiated preferences. In Majumdar, M., editor, Equilibrium and Dynamics, Essays in Honor of David Gale. London: McMillan. Roberts, D.~J. and Postlewaite, A. (1976). The incentives for pricetaking behavior in large exchange economies. Econometrica, 4(1):115127. Roth, A.~E. (1982). Incentive compatibility in a market with indivisible goods. Economic Letters, 9:127132. Roth, A.~E. and Postlewaite, A. (1977). Weak versus strong domination in a market with indivisible goods. Journal of Mathematical Economics, 4(2):131  137. Shapley, L. and Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, pages 2337. von Neumann, J. (1953). A certain zerosum twopersons game equivalent to the optimal assignment problem. In Kuhn, H.~W. and Tucker, A.~W., editors, Contribution to the Theory of Games, pages 512. Princeton University Press. Yilmaz, O. (2010). The probabilistic serial mechanism with private endowments. Games and Economic Behavior, 69(2):475491. Zhou, L. (1990). On a conjecture by gale about onesided matching problems. Journal of Economic Theory, 52(1):123  135. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/66624 
Available Versions of this Item

Competitive Equilibrium in the Random Assignment Problem. (deposited 28 Aug 2015 05:13)
 Competitive Equilibrium in the Random Assignment Problem. (deposited 15 Sep 2015 06:56) [Currently Displayed]