IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v46y2017i2d10.1007_s00182-016-0536-8.html
   My bibliography  Save this article

Scarcity, competition, and value

Author

Listed:
  • André Casajus

    (HHL Leipzig Graduate School of Management)

  • Harald Wiese

    (Universität Leipzig)

Abstract

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.

Suggested Citation

  • André Casajus & Harald Wiese, 2017. "Scarcity, competition, and value," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 295-310, May.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0536-8
    DOI: 10.1007/s00182-016-0536-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-016-0536-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-016-0536-8?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. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Mertens, J F, 1988. "The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages 1-65.
    3. Haimanko, Ori, 2001. "Cost sharing: the nondifferentiable case," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 445-462, June.
    4. Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167, Elsevier.
    5. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    6. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Other publications TiSEM 2c502ef8-76f0-47f5-ab45-1, Tilburg University, School of Economics and Management.
    3. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    4. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    5. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    6. Omer Edhan, 2013. "Values of nondifferentiable vector measure games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 947-972, November.
    7. Juan Vidal-Puga, 2017. "On the effect of taxation in the online sports betting market," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 8(2), pages 145-175, June.
    8. Calvo, E. & Santos, J. C., 2001. "Prices in Mixed Cost Allocation Problems," Games and Economic Behavior, Elsevier, vol. 37(2), pages 243-258, November.
    9. Avishay Aiche & Anna Rubinchik & Benyamin Shitovitz, 2015. "The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 135-151, February.
    10. Welter, Dominik & Napel, Stefan, 2016. "Responsibility-based allocation of cartel damages," VfS Annual Conference 2016 (Augsburg): Demographic Change 145886, Verein für Socialpolitik / German Economic Association.
    11. Chen Chen & Garud Iyengar & Ciamac C. Moallemi, 2013. "An Axiomatic Approach to Systemic Risk," Management Science, INFORMS, vol. 59(6), pages 1373-1388, June.
    12. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    13. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.
    14. Boonen, Tim J. & Tsanakas, Andreas & Wüthrich, Mario V., 2017. "Capital allocation for portfolios with non-linear risk aggregation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 95-106.
    15. Abraham Neyman & Rann Smorodinsky, 2003. "Asymptotic Values of Vector Measure Games," Discussion Paper Series dp344, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Marco Faravelli & Randall Walsh, 2011. "Smooth Politicians And Paternalistic Voters: A Theory Of Large Elections," Levine's Working Paper Archive 786969000000000250, David K. Levine.
    17. Ding, Zhanwen & Shi, Guiping, 2009. "Cooperation in a dynamical adjustment of duopoly game with incomplete information," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 989-993.
    18. Jhinyoung Shin & Rajdeep Singh, 2010. "Corporate Disclosures: Strategic Donation of Information," International Review of Finance, International Review of Finance Ltd., vol. 10(3), pages 313-337, September.
    19. Mario Guajardo & Kurt Jörnsten & Mikael Rönnqvist, 2016. "Constructive and blocking power in collaborative transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 25-50, January.
    20. Sylvie Thoron, 2016. "Morality Beyond Social Preferences: Smithian Sympathy, Social Neuroscience and the Nature of Social Consciousness [La moralité au delà des préférences sociales. La sympathie Smithienne, les neurosc," Post-Print hal-01645043, HAL.

    More about this item

    Keywords

    TU game; Shapley value; Lovász extension; Strong monotonicity; Partnership; Vector measure game; Mertens value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:46:y:2017:i:2:d:10.1007_s00182-016-0536-8. 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.