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Minimum incoming cost rules for arborescences

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  • Eric Bahel

    (Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    (University of Windsor)

Abstract

The paper examines minimum cost arborescence (mca) problems, which generalize the well-known minimum cost spanning tree (mcst) problems by allowing the cost to depend on the direction of the flow. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods are called minimum incoming cost rules for arborescences (MICRAs). They include as a particular case the extension of the folk solution introduced by Dutta and Mishra [Games Econ Behav 74(1):120–143, 2012], providing a simple procedure for its computation. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the Dutta–Mishra solution. Finally, we closely examine two MICRAs that (unlike the Dutta–Mishra rule) compensate agents who help others connect at a lower cost. The first of these two rules relates to the cycle-complete solution for mcst problems introduced by Trudeau [Games Econ Behav 75(1):402–412, 2012].

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2017. "Minimum incoming cost rules for arborescences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 287-314, August.
    • Handle: RePEc:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1061-9
    DOI: 10.1007/s00355-017-1061-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
    5. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    6. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    7. 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.
    8. Christian Trudeau, 2013. "Characterizations Of The Kar And Folk Solutions For Minimum Cost Spanning Tree Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-16.
    9. 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.
    10. Eric Bahel, 2014. "On the core and bargaining set of a veto game," Working Papers e07-48, Virginia Polytechnic Institute and State University, Department of Economics.
    11. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    12. 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.
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    Cited by:

    1. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    2. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
    3. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2020. "Stability in shortest path problems," MPRA Paper 98504, University Library of Munich, Germany.
    4. Bahel, Eric & Trudeau, Christian, 2019. "Stability and fairness in the job scheduling problem," Games and Economic Behavior, Elsevier, vol. 117(C), pages 1-14.
    5. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    6. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).

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