IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v42y2013i2p439-460.html
   My bibliography  Save this article

A discrete cost sharing model with technological cooperation

Author

Listed:
  • Eric Bahel
  • Christian Trudeau

Abstract

This article proposes a setting that allows for technological cooperation in the cost sharing model. Dealing with discrete demands, we study two properties: additivity and dummy. We show that these properties are insufficient to guarantee a unit-flow representation similar to that of Wang (Econ Lett 64:187–192, 1999 ). To obtain a characterization of unit flows, we strengthen the dummy axiom and introduce a property that requires the cost share of every agent to be non-decreasing in the incremental costs generated by their demand. Finally, a fairness requirement as to the compensation of technological cooperation is examined. Copyright Springer-Verlag 2013

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 439-460, May.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:2:p:439-460
    DOI: 10.1007/s00182-012-0320-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-012-0320-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-012-0320-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yves Sprumont, 2005. "On the Discrete Version of the Aumann-Shapley Cost-Sharing Method," Econometrica, Econometric Society, vol. 73(5), pages 1693-1712, September.
    2. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
    3. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
    4. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    5. J A Aloysius & E C Rosenthal, 1999. "The selection of joint projects by a consortium: Cost sharing mechanisms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1244-1251, December.
    6. Jelnov, Artyom & Tauman, Yair, 2009. "The private value of a patent: A cooperative approach," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 84-97, July.
    7. 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.
    8. Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 501-518, August.
    9. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
    10. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August.
    11. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
    12. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    13. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    2. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    3. Albizuri, M.J. & Díez, H. & Sarachu, A., 2014. "Monotonicity and the Aumann–Shapley cost-sharing method in the discrete case," European Journal of Operational Research, Elsevier, vol. 238(2), pages 560-565.
    4. Eric Bahel & Christian Trudeau, 2018. "Consistency requirements and pattern methods in cost sharing problems with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 737-765, September.
    5. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    6. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    7. Eric Bahel & Christian Trudeau, 2013. "Independence of dummy units and Shapley-Shubik methods in cost sharing problems with technological cooperation," Working Papers 1304, University of Windsor, Department of Economics.
    8. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    9. Bahel, Eric & Trudeau, Christian, 2019. "A cost sharing example in which subsidies are necessary for stability," Economics Letters, Elsevier, vol. 185(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    2. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 155-184, June.
    3. Yves Sprumont, 2010. "An Axiomatization of the Serial Cost-Sharing Method," Econometrica, Econometric Society, vol. 78(5), pages 1711-1748, September.
    4. EHLERS, Lars & WESTKAMP, Alexander, 2011. "Strategy-Proof Tie-Breaking," Cahiers de recherche 2011-07, Universite de Montreal, Departement de sciences economiques.
    5. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    6. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
    7. Eric Bahel & Christian Trudeau, 2018. "Consistency requirements and pattern methods in cost sharing problems with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 737-765, September.
    8. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    9. Bahel, Eric & Haller, Hans, 2013. "Cycles with undistinguished actions and extended Rock–Paper–Scissors games," Economics Letters, Elsevier, vol. 120(3), pages 588-591.
    10. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 551-589, August.
    11. Eric Bahel & Christian Trudeau, 2014. "Shapley–Shubik methods in cost sharing problems with technological cooperation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 261-285, August.
    12. Derks, Jean, 2005. "A new proof for Weber's characterization of the random order values," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 327-334, May.
    13. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
    14. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October.
    15. Calvo, E. & Santos, J. C., 2001. "Prices in Mixed Cost Allocation Problems," Games and Economic Behavior, Elsevier, vol. 37(2), pages 243-258, November.
    16. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    17. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    18. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    19. Moulin, Herve & Vohra, Rakesh, 2003. "Characterization of additive cost sharing methods," Economics Letters, Elsevier, vol. 80(3), pages 399-407, September.
    20. Friedman, Eric J., 2012. "Asymmetric Cost Sharing mechanisms," Games and Economic Behavior, Elsevier, vol. 75(1), pages 139-151.

    More about this item

    Keywords

    Cost sharing; Demand; Technology; Cooperation; Flow methods; C71; D63;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:42:y:2013:i:2:p:439-460. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.