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Paths to stable allocations

Author

Listed:
  • Agnes Cseh

    (Hungarian Academy of Sciences, Centre for Economic and Regional Studies, Institute of Economics)

  • Martin Skutella

    (TU Berlin, Institut für Mathematik, Germany)

Abstract

The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation instances. In this setting, a feasible allocation is given and the aim is to reach a stable allocation by raising the value of the allocation along blocking edges and reducing it on worse edges if needed. Do such myopic changes lead to a stable solution? In our present work, we analyze both better and best response dynamics from an algorithmic point of view. With the help of two deterministic algorithms we show that random procedures reach a stable solution with probability one for all rational input data in both cases. Surprisingly, while there is a polynomial path to stability when better response strategies are played (even for irrational input data), the more intuitive best response steps may require exponential time. We also study the special case of correlated markets. There, random best response strategies lead to a stable allocation in expected polynomial time.

Suggested Citation

  • Agnes Cseh & Martin Skutella, 2018. "Paths to stable allocations," CERS-IE WORKING PAPERS 1820, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1820
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    stable matching; stable allocation; paths to stability; best response strategy; better response strategy; correlated market;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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