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Axiomatizations of the proportional Shapley value

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  • Manfred Besner

    (HFT Stuttgart, University of Applied Sciences)

Abstract

We present new axiomatic characterizations of the proportional Shapley value, a weighted TU-value with the worths of the singletons as weights. The presented characterizations are proportional counterparts to the famous characterizations of the Shapley value by Shapley (Contributions to the theory of games, vol. 2. Princeton University Press, Princeton, pp 307–317, 1953b) and Young (Cost allocation: methods, principles, applications. North Holland Publishing Co, 1985a). We introduce two new axioms, called proportionality and player splitting, respectively. Each of them makes a main difference between the proportional Shapley value and the Shapley value. If the stand-alone worths are plausible weights, the proportional Shapley value is a convincing alternative to the Shapley value, for example in cost allocation. Especially, the player splitting property, which states that players’ payoffs do not change if another player splits into two new players who have the same impact to the game as the original player, justifies the use of the proportional Shapley value in many economic situations.

Suggested Citation

  • Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    • Handle: RePEc:kap:theord:v:86:y:2019:i:2:d:10.1007_s11238-019-09687-7
    DOI: 10.1007/s11238-019-09687-7
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    1. Mingming Leng & Mahmut Parlar, 2009. "Allocation of Cost Savings in a Three-Level Supply Chain with Demand Information Sharing: A Cooperative-Game Approach," Operations Research, INFORMS, vol. 57(1), pages 200-213, February.
    2. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    3. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    4. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    5. 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.
    6. Frank Huettner, 2015. "A proportional value for cooperative games with a coalition structure," Theory and Decision, Springer, vol. 78(2), pages 273-287, February.
    7. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    10. Gangolly, Js, 1981. "On Joint Cost Allocation - Independent Cost Proportional Scheme (Icps) And Its Properties," Journal of Accounting Research, Wiley Blackwell, vol. 19(2), pages 299-312.
    11. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    12. Roth, Ae & Verrecchia, Re, 1979. "Shapley Value As Applied To Cost Allocation - Reinterpretation," Journal of Accounting Research, Wiley Blackwell, vol. 17(1), pages 295-303.
    13. Tijs, Stef H. & Driessen, Theo S. H., 1986. "Extensions of solution concepts by means of multiplicative [var epsilon]-tax games," Mathematical Social Sciences, Elsevier, vol. 12(1), pages 9-20, August.
    14. Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
    15. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    16. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
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    Citations

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    Cited by:

    1. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    2. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    3. Besner, Manfred, 2019. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi payoff," MPRA Paper 92247, University Library of Munich, Germany.
    4. Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    5. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    6. Besner, Manfred, 2019. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," MPRA Paper 92771, University Library of Munich, Germany.
    7. Manfred Besner, 2020. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 193-212, June.
    8. Ying Wang & Xiangyu Mao & Hashim Zameer, 2022. "Designing benefit distribution driven innovation strategy for local enterprises under the global value chain system," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 2358-2373, September.
    9. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    10. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    11. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
    12. Yakubu, Hanan & Kwong, C.K., 2021. "Forecasting the importance of product attributes using online customer reviews and Google Trends," Technological Forecasting and Social Change, Elsevier, vol. 171(C).
    13. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    14. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    15. Besner, Manfred, 2020. "Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations," MPRA Paper 99355, University Library of Munich, Germany.
    16. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    17. Wenzhong Li & Genjiu Xu & Hao Sun, 2020. "Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    18. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 107615, University Library of Munich, Germany.
    19. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 106638, University Library of Munich, Germany.
    20. Mallozzi, Lina & Vidal-Puga, Juan, 2024. "An efficient Shapley value for games with fuzzy characteristic function," MPRA Paper 122168, University Library of Munich, Germany.
    21. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.
    22. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.

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