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Demand operators and the Dutta–Kar rule for minimum cost spanning tree problems

Author

Listed:
  • Changyong Han

    (Korea SMEs and Startups Institute)

  • Bawoo Kim

    (Samsung Electronics)

  • Youngsub Chun

    (Seoul National University)

Abstract

Granot and Huberman (Math Program 29:323–347, 1984) introduced two demand operators, the weak demand operator and the strong demand operator, for minimum cost spanning tree problems, which are intended to measure the maximum amount that each agent can demand from her followers in compensation for making a link to her. We investigate the implications of these demand operators by introducing a procedure which enables us to sequentially calculate the maximum for each agent. On the irreducible cost matrix, by applying the weak demand operator sequentially to each agent, the Dutta–Kar allocation (Dutta and Kar in Games Econ Behav 48:223–248, 2004) is obtained if the procedure is initiated from any efficient allocation. For the strong demand operator, the Dutta–Kar allocation is obtained if the procedure is initiated from any allocation in the irreducible core.

Suggested Citation

  • Changyong Han & Bawoo Kim & Youngsub Chun, 2024. "Demand operators and the Dutta–Kar rule for minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 101-124, August.
    • Handle: RePEc:spr:joecth:v:78:y:2024:i:1:d:10.1007_s00199-023-01526-9
    DOI: 10.1007/s00199-023-01526-9
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    Keywords

    Minimum cost spanning tree problems; Demand operators; Irreducible cost matrix; Dutta–Kar rule; Prim algorithm;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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