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Semi-stability in roommate problems

Author

Listed:
  • Herings, P. Jean-Jacques

    (Department of Econometrics and Operations Research, Tilburg University)

  • Zhou, Yu

    (Department of Economics, Graduate School of Economics, Nagoya University)

Abstract

We study the roommate problem allowing for preferences with indifferences and agents remaining single. A stable outcome need not exist. We introduce semi-stability, a novel notion that guarantees existence and restores stability through minimal policy or group interventions. We build an equilibrium foundation for semi-stability by showing its equivalence to a newly proposed choice-based equilibrium concept. We show that undominated semi-stable outcomes are Pareto optimal and under strict preferences, every semi-stable outcome is Pareto optimal. Nevertheless, standard structural properties, such as the rural hospital theorem and the lattice properties, fail for semi-stable outcomes. We also discuss possible applications.

Suggested Citation

  • Herings, P. Jean-Jacques & Zhou, Yu, 0. "Semi-stability in roommate problems," Theoretical Economics, Econometric Society.
    • Handle: RePEc:the:publsh:6562
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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