IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v186y2011i1p263-27410.1007-s10479-011-0897-0.html
   My bibliography  Save this article

Regression games

Author

Listed:
  • Miklós Pintér

Abstract

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payoff (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall fit, i.e. the fit of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young’s (Int. J. Game Theory 14:65–72, 1985 ) axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Miklós Pintér, 2011. "Regression games," Annals of Operations Research, Springer, vol. 186(1), pages 263-274, June.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:263-274:10.1007/s10479-011-0897-0
    DOI: 10.1007/s10479-011-0897-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0897-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0897-0?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. Conklin, Michael & Powaga, Ken & Lipovetsky, Stan, 2004. "Customer satisfaction analysis: Identification of key drivers," European Journal of Operational Research, Elsevier, vol. 154(3), pages 819-827, May.
    2. Stan Lipovetsky & Michael Conklin, 2001. "Analysis of regression in game theory approach," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(4), pages 319-330, October.
    3. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    4. Ulrike Grömping & Sabine Landau, 2010. "Do not adjust coefficients in Shapley value regression," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 194-202, March.
    5. Stan Lipovetsky, 2008. "Surf — Structural Unduplicated Reach And Frequency: Latent Class Turf And Shapley Value Analyses," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 203-216.
    6. W. Michael Conklin & Stan Lipovetsky, 2005. "Marketing Decision Analysis By Turf And Shapley Value," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 5-19.
    7. Feldman, Barry, 2007. "A Theory of Attribution," MPRA Paper 3349, University Library of Munich, Germany, revised 29 May 2007.
    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. Karl Michael Ortmann, 2016. "The link between the Shapley value and the beta factor," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 311-325, November.

    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. Lipovetsky, Stan & Conklin, Michael, 2014. "Finding items cannibalization and synergy by BWS data," Journal of choice modelling, Elsevier, vol. 12(C), pages 1-9.
    2. Stan Lipovetsky & Igor Mandel, 2017. "Coefficients of Structural Association," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 285-313, March.
    3. Riccardo Colini-Baldeschi & Marco Scarsini & Stefano Vaccari, 2018. "Variance Allocation and Shapley Value," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 919-933, September.
    4. Borgonovo, Emanuele & Plischke, Elmar & Rabitti, Giovanni, 2024. "The many Shapley values for explainable artificial intelligence: A sensitivity analysis perspective," European Journal of Operational Research, Elsevier, vol. 318(3), pages 911-926.
    5. Molina, Elisenda & Tejada, Juan, 2013. "The Shapley group value," DES - Working Papers. Statistics and Econometrics. WS ws133430, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Stan Lipovetsky & W. Michael Conklin, 2015. "Predictor relative importance and matching regression parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 1017-1031, May.
    7. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    8. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    9. Pera, Rebecca & Viglia, Giampaolo & Furlan, Roberto, 2016. "Who Am I? How Compelling Self-storytelling Builds Digital Personal Reputation," Journal of Interactive Marketing, Elsevier, vol. 35(C), pages 44-55.
    10. Hugh Chen & Scott M. Lundberg & Su-In Lee, 2022. "Explaining a series of models by propagating Shapley values," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    11. Emrah Arbak, 2017. "Identifying the provisioning policies of Belgian banks," Working Paper Research 326, National Bank of Belgium.
    12. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
    13. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    14. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
    15. Xingwei Hu, 2020. "A theory of dichotomous valuation with applications to variable selection," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1075-1099, November.
    16. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the shapley value: a new approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 153-167, February.
    17. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    18. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2019. "Interaction indices for multichoice games," Documents de travail du Centre d'Economie de la Sorbonne 19019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    19. Dmitry Sharapov & Paul Kattuman & Diego Rodriguez & F. Javier Velazquez, 2021. "Using the SHAPLEY value approach to variance decomposition in strategy research: Diversification, internationalization, and corporate group effects on affiliate profitability," Strategic Management Journal, Wiley Blackwell, vol. 42(3), pages 608-623, March.
    20. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.

    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:annopr:v:186:y:2011:i:1:p:263-274:10.1007/s10479-011-0897-0. 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.