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An incompatibility between recursive unanimity and strategy-proofness in two-sided matching problems

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Abstract

In this article, we study the incompatibilities for the properties on matching rules in two-sided many-to-one matching problems under responsive preferences. We define a new property called respect for recursive unanimity. This property requires that if every agent matches with its first choice among its really possible choices that are based on a recursive procedure like the well-known top trading cycles algorithm, then we should respect it. More precisely, given a matching problem, we exclude the agents whose first choices are satisfied without any discrepancy among them, and consider the restricted matching problems of the remaining agents. If we reach a state in which all agents are excluded by repeating this procedure, then we should respect the outcome. This property is weaker than stability and is stronger than respect for unanimity (that is also known as weak unanimity). We show that there are no strategy-proof matching rules that respect recursive unanimity.

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References

  • Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93: 729–747

    Article  Google Scholar 

  • Abdulkadiroğlu A, Pathak P, Roth A (2005a) The New York city high school match. Am Econ Rev 95: 364–367

    Article  Google Scholar 

  • Abdulkadiroğlu A, Pathak P, Roth A, Sönmez T (2005b) The Boston public school match. Am Econ Rev 95(2): 368–372

    Article  Google Scholar 

  • Abdulkadiroğlu A, Pathak P, Roth A, Sönmez T (2006) Changing the Boston school choice mechanism. NBER Working Paper No. 11965

  • Abdulkadiroğlu A, Pathak P, Roth A (2009) Strategy-proofness versus efficiency in matching with indifferences: redesigning the NYC high school match. Am Econ Rev 99: 1954–1978

    Article  Google Scholar 

  • Alcalde J, Barberà S (1994) Top dominance and the possibility of strategy-proof stable solutions to matching problems. Econ Theory 4: 417–435

    Article  Google Scholar 

  • Balinski M, Sönmez T (1999) A tale of two mechanisms: student placement. J Econ Theory 84: 73–94

    Article  Google Scholar 

  • Eeckhout J (2000) On the uniqueness of stable marriage matchings. Econ Lett 69: 1–8

    Article  Google Scholar 

  • Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Monthly 69: 9–15

    Article  Google Scholar 

  • Knuth DE (1976) Marriages Stables. Les Presses de I’Universite de Montreal, Montreal

    Google Scholar 

  • Roth AE (1982) The economics of matching: stability and incentives. Math Oper Res 7: 617–628

    Article  Google Scholar 

  • Roth AE (1984) The evolution of the labor market for medical interns and residents: a case study in game theory. J Polit Econ 92: 991–1016

    Article  Google Scholar 

  • Roth AE (1985) The college admissions problem is not equivalent to the marriage problem. J Econ Theory 36: 277–288

    Article  Google Scholar 

  • Roth AE (2003) The origins, history, and design of the resident match. J Am Med Assoc 289: 909–912

    Article  Google Scholar 

  • Roth AE, Peranson E (1997) The effects of the change in the NRMP matching algorithm. J Am Med Assoc 278: 729–732

    Article  Google Scholar 

  • Roth AE, Peranson E (1999) The redesign of the matching market for american physicians: some engineering aspects of economic design. Am Econ Rev 89: 748–780

    Article  Google Scholar 

  • Sasaki H, Toda M (1992) Consistency and characterization of the two-sided matching problems. J Econ Theory 56: 218–227

    Article  Google Scholar 

  • Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1: 23–37

    Article  Google Scholar 

  • Sönmez T (1996) Strategy-proofness in many-to-one matching problems. Econ Des 1: 365–380

    Google Scholar 

  • Sönmez T (1999) Strategy-proofness and essentially single-valued core. Econometrica 67: 677–689

    Article  Google Scholar 

  • Tadenuma K, Toda M (1998) Implementable stable solutions to pure matching problems. Math Soc Sci 35: 121–132

    Article  Google Scholar 

  • Takagi S, Serizawa S (2010) An impossibility theorem for matching problems. Soc Choice Welf. doi:10.1007/s00355-009-0439-8

  • Toda M (2006) Monotonicity and consistency in matching markets. Int J Game Theory 34: 13–31

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Political Science and Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Takumi Kongo

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  1. Takumi Kongo
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Correspondence to Takumi Kongo.

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Kongo, T. An incompatibility between recursive unanimity and strategy-proofness in two-sided matching problems. Soc Choice Welf 40, 461–478 (2013). https://doi.org/10.1007/s00355-011-0615-5

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  • DOI: https://doi.org/10.1007/s00355-011-0615-5

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