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

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Mumcu, Ayse
Saglam, Ismail

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

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Li, Hao & Rosen, Sherwin, 1998. "Unraveling in Matching Markets," American Economic Review, American Economic Association, vol. 88(3), pages 371-87, June. [Downloadable!] (restricted)
  2. Hideo Konishi & M. Utku Unver, 2001. "Games of Capacity Manipulation in Hospital-Intern Markets," Boston College Working Papers in Economics 515, Boston College Department of Economics, revised 31 Jul 2002. [Downloadable!]
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November. [Downloadable!] (restricted)
  6. 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.
  7. 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. [Downloadable!] (restricted)
  8. Haruvy, Ernan & Roth, Alvin E. & Unver, M. Utku, 2006. "The dynamics of law clerk matching: An experimental and computational investigation of proposals for reform of the market," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 457-486, March. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  10. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September. [Downloadable!] (restricted)
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