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Connection problems in mountains and monotonic allocation schemes

Author

Listed:
  • Stefano Moretti

    ()

  • Henk Norde

    ()

  • Kim Pham Do

    ()

  • Stef Tijs

    ()

Abstract

Directed minimum cost spanning tree problems of a special kind are studied,namely those which show up in considering the problem of connecting units (houses)in mountains with a purifier.For such problems an easy method is described to obtain a minimum cost spanning tree.The related cost sharing problem is tackled by considering thecorresponding cooperative cost game with the units as players and also the related connection games,for each unit one.The cores of the connection games have a simple structure and each core element can be extended to a population monotonic allocation scheme (pmas)and also to a bi-monotonic allocation scheme.These pmas-es for the connection games result in pmas-es for the cost game.
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Suggested Citation

  • Stefano Moretti & Henk Norde & Kim Pham Do & Stef Tijs, 2002. "Connection problems in mountains and monotonic allocation schemes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 83-99, June.
  • Handle: RePEc:spr:topjnl:v:10:y:2002:i:1:p:83-99
    DOI: 10.1007/BF02578942
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    File URL: http://hdl.handle.net/10.1007/BF02578942
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    References listed on IDEAS

    as
    1. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
    2. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    3. Maurice Salles, 2005. "Social Choice," Post-Print halshs-00337075, HAL.
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    Citations

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    Cited by:

    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Discussion Paper 2003-129, Tilburg University, Center for Economic Research.
    3. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Discussion Paper 2005-3, Tilburg University, Center for Economic Research.
    4. Tijs, Stef & Branzei, Rodica & Moretti, Stefano & Norde, Henk, 2006. "Obligation rules for minimum cost spanning tree situations and their monotonicity properties," European Journal of Operational Research, Elsevier, vol. 175(1), pages 121-134, November.
    5. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-016-0561-7 is not listed on IDEAS
    6. repec:dau:papers:123456789/4879 is not listed on IDEAS
    7. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.

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