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Games of capacity allocation in many-to-one matching with an aftermarket

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  • Mumcu, Ayse
  • Saglam, Ismail

Abstract

In this paper, we study many-to-one matching (hospital-intern markets) with an aftermarket. We analyze the Nash equilibria of capacity allocation games, in which preferences of hospitals and interns are common knowledge and every hospital determines a quota for the regular market given its total capacity for the two matching periods. Under the intern-optimal stable matching system, we show that a pure-strategy Nash equilibrium may not exist. Common preferences for hospitals ensure the existence of equilibrium in weakly dominant strategies whereas unlike in games of capacity manipulation strong monotonicity of population is not a sufficient restriction on preferences to avoid the nonexistence problem. Besides, in games of capacity allocation, it is not true either that every hospital weakly prefers a mixed-strategy Nash equilibrium to any larger regular market quota profiles.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9239.

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Date of creation: 19 Jun 2008
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Handle: RePEc:pra:mprapa:9239

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Keywords: Many-to-one matching; hospital-intern market; aftermarket; capacity allocation game;

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  1. Sonmez, Tayfun, 1999. "Can Pre-arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, Elsevier, vol. 86(1), pages 148-156, May.
  2. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  3. Hao Li & Wing Suen, 2000. "Risk Sharing, Sorting, and Early Contracting," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 1058-1087, October.
  4. Guillaume R. Fréchette & Alvin E. Roth & M. Utku Ünver, 2007. "Unraveling yields inefficient matchings: evidence from post-season college football bowls," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 967-982, December.
  5. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  6. Li, Hao & Rosen, Sherwin, 1998. "Unraveling in Matching Markets," American Economic Review, American Economic Association, vol. 88(3), pages 371-87, June.
  7. Fuhito Kojima, 2006. "Mixed Strategies in Games of Capacity Manipulation in Hospital–Intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 25-28, August.
  8. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
  9. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  10. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 3-24, August.
  11. Ernan Haruvy & Alvin E. Roth & M. Utku Unver, 2004. "The Dynamics of Law Clerk Matching: An Experimental and Computational Investigation of Proposals for Reform of the Market," Experimental 0404001, EconWPA.
  12. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  13. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
  14. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
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Cited by:
  1. Antonio Romero-Medina & Matteo Triossi, 2011. "Games with capacity manipulation : incentives and Nash equilibria," Economics Working Papers we1125, Universidad Carlos III, Departamento de Economía.
  2. Azevedo, Eduardo M., 2014. "Imperfect competition in two-sided matching markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 207-223.

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