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Marginal Games and Characterizations of the Shapley Value in TU Games

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Game Theory and Applications (China GTA 2016, China-Dutch GTA 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 758))

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Abstract

Axiomatizations and recursive representations of the Shapley value on the class of all cooperative games with transferable utilities are given. Marginal games, which are closely related to dual games, play central roles in our results. Our axiomatizations are based on axioms that are marginal game variations of the well-known balanced contributions property, so that they are interpreted as fair treatment between two players in games as the balanced contributions property is. Our general recursive representation enables us to represent the Shapley value for n-person games by those for r-person and \((n-r)\)-person games with fixed \(r<n\). The particular case of \(r=1\) has a clear contrasting interpretation to the existing recursive formula.

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References

  1. Branzei, R., Fragnelli, V., Tijs, S.: Tree-connected peer group situations and peer group games. Math. Methods Oper. Res. 55, 93–106 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Branzei, R., Dimitrov, D., Tijs, S.: Models in Cooperative Game Theory, 2nd edn. Springer-Verlag, Heidelberg (2008)

    MATH  Google Scholar 

  3. Branzei, R., Fragnelli, V., Meca, A., Tijs, S.: On cooperative games related to market situations and auctions. Int. Game Theor. Rev. 11, 459–470 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. van den Brink, R., Chun, Y., Funaki, Y., Park, B.: Consistency, population solidarity, and egalitarian solutions for TU-games. Theor. Decis. 81(3), 427–447 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chun, Y.: A new axiomatization of the Shapley value. Games Econ. Behav. 1, 119–130 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dehez, P.: Allocation of fixed costs: characterization of the (dual) weighted Shapley value. Int. Game Theor. Rev. 13, 141–157 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Derks, J.J.M., Haller, H.H.: Null players out? linear values for games with variable supports. Int. Game Theor. Rev. 1, 301–314 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Driessen, T.: The greedy bankruptcy game: an alternative game theoretic analysis of a bankruptcy problem. In: Petrosjan, L., Mazalov, V. (eds.) Game Theory and Application, vol. IV, pp. 45–61. Nova Science Publishers Inc., New York (1998)

    Google Scholar 

  9. Dutta, B., Ray, D.: A concept of egalitarianism under participation constraint. Econometrica 57, 615–635 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hart, S., Mas-Colell, A.: Potential, value and consistency. Econometrica 57, 589–614 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Maschler, M., Owen, G.: The consistent Shapley value for hyperplane games. Int. J. Game Theor. 18, 389–407 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Myerson, R.B.: Conference structures and fair allocation rules. Int. J. Game Theor. 9, 169–182 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  13. Oishi, T., Nakayama, M., Hokari, T., Funaki, Y.: Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations. J. Math. Econ. 63, 44–53 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pérez-Castrillo, D., Wettstein, D.: Bidding for the surplus: a non-cooperative approach to the Shapley value. J. Econ. Theor. 100, 274–294 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Shapley, L.S.: A value for \(n\)-person games. In: Kuhn, H., Tucker, A. (eds.) Contributions to the Theory of Games, vol.II, pp. 307–317. Princeton University Press, Princeton (1953)

    Google Scholar 

  16. Sprumont, Y.: Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ. Behav. 2, 378–394 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tijs, S.H., Driessen, T.S.: Extensions of solution concepts by means of multiplicative \(\epsilon \)-tax game. Math. Soc. Sci. 12, 9–20 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Young, H.: Power, prices, and incomes in voting systems. Math. Program. 14, 129–148 (1978)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors thank Rodica Branzei, Irinel Dragan, and Stef Tijs for their helpful comments. This work was supported by JSPS KAKENHI Grant Number 15K17031 (Kongo), 24220033 (Funaki), 26245026 (Funaki), and 26380247 (Funaki).

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Authors and Affiliations

  1. Faculty of Economics, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka, 814-0180, Japan

    Takumi Kongo

  2. School of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Yukihiko Funaki

Authors
  1. Takumi Kongo
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  2. Yukihiko Funaki
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Correspondence to Yukihiko Funaki .

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Editors and Affiliations

  1. Fuzhou University, Fuzhou, Fujian, China

    Deng-Feng Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiao-Guang Yang

  3. University of Twente, Enschede, The Netherlands

    Marc Uetz

  4. Northwestern Polytechnical University, Xi'an, China

    Gen-Jiu Xu

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Kongo, T., Funaki, Y. (2017). Marginal Games and Characterizations of the Shapley Value in TU Games. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_12

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  • DOI: https://doi.org/10.1007/978-981-10-6753-2_12

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6752-5

  • Online ISBN: 978-981-10-6753-2

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