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A Non-Cooperative Approach to the Folk Rule in Minimum Cost Spanning Tree Problems

Author

Listed:
  • Hernández, Penélope

    (Departamento de Análisis Económico and ERI-CES)

  • Josep E., Peris

    (University of Alicante, D. Quantitative Methods and Economic Theory)

  • Vidal-Puga, Juan

    (Department of Statistics and Operations Research)

Abstract
This paper deals with the problem of finding a way to distribute the cost of a minimum cost spanning tree problem between the users. A rule that assigns a payoff to each agent provides this distribution. An optimistic point of view is considered to devise a cooperative game. Following this optimistic approach, a sequential game exerts this construction to define the action sets of the agents. The main result states the existence of a unique cost allocation in subgame perfect equilibria. This cost allocation matches the one suggested by the folk rule.

Suggested Citation

  • Hernández, Penélope & Josep E., Peris & Vidal-Puga, Juan, 2019. "A Non-Cooperative Approach to the Folk Rule in Minimum Cost Spanning Tree Problems," QM&ET Working Papers 19-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    • Handle: RePEc:ris:qmetal:2019_005
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    References listed on IDEAS

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    1. Hougaard, Jens Leth & Tvede, Mich, 2012. "Truth-telling and Nash equilibria in minimum cost spanning tree models," European Journal of Operational Research, Elsevier, vol. 222(3), pages 566-570.
    2. 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.
    3. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    4. Mutuswami, Suresh & Winter, Eyal, 2002. "Subscription Mechanisms for Network Formation," Journal of Economic Theory, Elsevier, vol. 106(2), pages 242-264, October.
    5. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems," Other publications TiSEM 56ea8c64-a05f-4b3f-ab61-9, Tilburg University, School of Economics and Management.
    6. Hernández, Penélope & Peris, Josep E. & Silva-Reus, José A., 2016. "Strategic sharing of a costly network," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 72-82.
    7. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    8. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems," Discussion Paper 1994-106, Tilburg University, Center for Economic Research.
    9. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
    10. Moulin, Hervé & Velez, Rodrigo A., 2013. "The price of imperfect competition for a spanning network," Games and Economic Behavior, Elsevier, vol. 81(C), pages 11-26.
    11. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    12. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    13. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    14. Gustavo Bergantinos & Juan Vidal-Puga, 2008. "On Some Properties of Cost Allocation Rules in Minimum Cost Spanning Tree Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 251-267, December.
    15. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems : The proportional rule and the decentralized rule," Other publications TiSEM 2c6cd46b-7e72-4262-a479-3, Tilburg University, School of Economics and Management.
    16. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    17. Bag, Parimal Kanti & Winter, Eyal, 1999. "Simple Subscription Mechanisms for Excludable Public Goods," Journal of Economic Theory, Elsevier, vol. 87(1), pages 72-94, July.
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    Cited by:

    1. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.

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    More about this item

    Keywords

    Minimum cost spanning tree; cost allocation; subgame perfect equilibrium;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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