IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v47y1998i3p423-449.html
   My bibliography  Save this article

Conservation of energy in value theory

Author

Listed:
  • K. Ortmann

Abstract

The potential approach of value theory is extended with respect to a new characterizing property called conservation giving a clear interpretation of the potential. Many analogues between game theory and physics are presented. Particularly, there is a theorem of conservation of energy analogous to the highly important one in classical mechanics. Moreover, the Shapley-Value gets a new interpretation as the marginal contribution to a certain average in contrast to that as an average marginal contribution instead. The Banzhaf-Index can also be uniquely characterized by this approach. Finally, all results are extended to games with a continuum of players of finitely many types. Copyright Physica-Verlag 1998

Suggested Citation

  • K. Ortmann, 1998. "Conservation of energy in value theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 423-449, October.
  • Handle: RePEc:spr:mathme:v:47:y:1998:i:3:p:423-449
    DOI: 10.1007/BF01198404
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF01198404
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/BF01198404?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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    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. Takaaki Abe & Satoshi Nakada, 2023. "Potentials and solutions of cooperative games with a fixed player set," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 757-774, September.
    2. Andr'e Casajus & Yukihiko Funaki & Frank Huettner, 2024. "Random partitions, potential, value, and externalities," Papers 2402.00394, arXiv.org, revised Jun 2024.
    3. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    4. Judith Timmer & Peter Borm & Stef Tijs, 2004. "On three Shapley-like solutions for cooperative games with random payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 595-613, August.
    5. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    6. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    7. Casajus, André & Huettner, Frank, 2018. "Calculating direct and indirect contributions of players in cooperative games via the multi-linear extension," Economics Letters, Elsevier, vol. 164(C), pages 27-30.
    8. Casajus, André & Huettner, Frank, 2018. "Decomposition of solutions and the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 37-48.
    9. Casajus, André & Huettner, Frank, 2015. "Potential, value, and the multilinear extension," Economics Letters, Elsevier, vol. 135(C), pages 28-30.
    10. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    11. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    12. Karl Ortmann, 2013. "A cooperative value in a multiplicative model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 561-583, September.
    13. Casajus, André, 2014. "Potential, value, and random partitions," Economics Letters, Elsevier, vol. 125(2), pages 164-166.
    14. Kurz, Sascha & Mayer, Alexander & Napel, Stefan, 2021. "Influence in weighted committees," European Economic Review, Elsevier, vol. 132(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. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    2. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    3. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
    4. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    5. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    6. Alexandre Skoda & Xavier Venel, 2022. "Weighted Average-convexity and Cooperative Games," Documents de travail du Centre d'Economie de la Sorbonne 22016, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Nir Dagan, 1995. "Consistent Solutions in Exchange Economies: a Characterization of the Price Mechanism," Economic theory and game theory 011, Nir Dagan.
    8. Walter Beckert, 2018. "An Empirical Analysis of Countervailing Power in Business-to-Business Bargaining," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 52(3), pages 369-402, May.
    9. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    10. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
    11. Casajus, André & Huettner, Frank, 2015. "Potential, value, and the multilinear extension," Economics Letters, Elsevier, vol. 135(C), pages 28-30.
    12. Casajus, André, 2014. "Potential, value, and random partitions," Economics Letters, Elsevier, vol. 125(2), pages 164-166.
    13. Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers wp2007_0709, CEMFI.
    14. repec:ebl:ecbull:v:3:y:2008:i:70:p:1-8 is not listed on IDEAS
    15. Gomes, Armando & Hart, Sergiu & Mas-Colell, Andreu, 1999. "Finite Horizon Bargaining and the Consistent Field," Games and Economic Behavior, Elsevier, vol. 27(2), pages 204-228, May.
    16. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "Reassignment-proof rules for land rental problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 173-193, March.
    17. Dequiedt, Vianney & Zenou, Yves, 2017. "Local and consistent centrality measures in parameterized networks," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 28-36.
    18. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    19. James R. Hines, Jr., 1990. "The Transfer Pricing Problem: Where the Profits Are," NBER Working Papers 3538, National Bureau of Economic Research, Inc.
    20. Grauwin, Sébastian & Goffette-Nagot, Florence & Jensen, Pablo, 2012. "Dynamic models of residential segregation: An analytical solution," Journal of Public Economics, Elsevier, vol. 96(1), pages 124-141.
    21. Ander Perez-Orive & Andrea Caggese, 2017. "Capital Misallocation and Secular Stagnation," 2017 Meeting Papers 382, Society for Economic Dynamics.

    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:mathme:v:47:y:1998:i:3:p:423-449. 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.