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Roth–Postlewaite stability and von Neumann–Morgenstern stability

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  • Kawasaki, Ryo

Abstract

In the framework of the indivisible goods market defined in Shapley and Scarf (1974), Roth and Postlewaite (1977) define an allocation to be (RP-)stable if no coalition of agents can benefit from a reallocation of goods after the allocation has been decided upon. In this paper, we show that the set of RP-stable allocations is the unique von Neumann–Morgenstern (vNM-) stable set of the following domination relation: an allocation y dominates x if there is a coalition S that blocks x using allocation y in the market with x as its initial endowment. This connection between the two stability concepts also carries over for the indivisible goods market with multiple types of Konishi et al. (2001).

Suggested Citation

  • Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.
  • Handle: RePEc:eee:mateco:v:58:y:2015:i:c:p:1-6
    DOI: 10.1016/j.jmateco.2015.02.002
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    References listed on IDEAS

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    1. Kamijo, Yoshio & Kawasaki, Ryo, 2010. "Dynamics, stability, and foresight in the Shapley-Scarf housing market," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 214-222, March.
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    Cited by:

    1. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2018. "Housing market models with consumption externalities," CSEF Working Papers 500, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Balbuzanov, Ivan & Kotowski, Maciej H., 2017. "Endowments, Exclusion, and Exchange," Working Paper Series rwp17-016, Harvard University, John F. Kennedy School of Government.

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