Le, Phuong (2013): Competitive Equilibrium in the Random Assignment Problem.
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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 
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