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Regression games

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  • 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
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    References listed on IDEAS

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    1. 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.
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    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.
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    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.

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