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Smith and Rawls Share a Room: Stability and Medians

Author

Listed:
  • Bettina Klaus

    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Flip Klijn

    (Institute for Economic Analysis (CSIC), Campus UAB, Barcelona, Spain)

Abstract

We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the "lone wolf" theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the so-called stable median matching theorem, showing how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems. Finally, we extend our results to two-sided matching problems.

Suggested Citation

  • Bettina Klaus & Flip Klijn, 2009. "Smith and Rawls Share a Room: Stability and Medians," Harvard Business School Working Papers 09-111, Harvard Business School.
    • Handle: RePEc:hbs:wpaper:09-111
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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