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The Shapley Valuation Function for Strategic Games in which Players Cooperate

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Abstract

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lower-value based method to associate coalitional games with strategic games that was introduced in Carpente et al. (2005). We discuss axiomatic characterizations of the Shapley valuation function.

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References

  • Carpente L, Casas-Méndez B, García-Jurado I, Van den Nouweland A (2005) Values for strategic games in which players cooperate. Int J Game Theory 33(3):397–419

    Article  MATH  Google Scholar 

  • Montero M (2000) Endogenous coalition formation and bargaining. PhD dissertation, CentER, Tilburg University.

  • Myerson RB (1980) Conference structures and fair allocation rules. Int J Game Theory 9:169–182

    Article  MATH  MathSciNet  Google Scholar 

  • Norde H, Voorneveld M (2004) Characterizations of the value of matrix games. Math Soc Sci 48:193–206

    Article  MATH  MathSciNet  Google Scholar 

  • Shapley LS (1953) A value for n-person games. Ann Math Stud 28:307–318

    MathSciNet  Google Scholar 

  • Shapley LS (1958) The solution of a symmetric market game. Ann Math Stud 40:145–162

    MathSciNet  Google Scholar 

  • Shapley LS, Shubik M (1969) On market games. J Econ Theory 1:9–25

    Article  MathSciNet  Google Scholar 

  • Van Damme E, Furth D (2002) Game theory and the market. In: Borm P, Peters H (eds) Chapters in game theory. Kluwer, Dordrecht, pp 51–81

    Google Scholar 

  • Von Neumann J, Morgenstern O (1953) Theory of games and economic behavior. Princeton University Press, (Ist edn, 1944), NJ, USA

    MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultade de Informática, Universidade da Coruña, 15071 A, Coruña, Spain

    Luisa Carpente

  2. Departamento de Estatística e IO, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Balbina Casas-Méndez & Ignacio García-Jurado

  3. Department of Economics, 435 PLC, University of Oregon, Eugene, OR, 97403-1285, USA

    Anne van den Nouweland

Authors
  1. Luisa Carpente
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  2. Balbina Casas-Méndez
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  3. Ignacio García-Jurado
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  4. Anne van den Nouweland
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Corresponding author

Correspondence to Anne van den Nouweland.

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Carpente, L., Casas-Méndez, B., García-Jurado, I. et al. The Shapley Valuation Function for Strategic Games in which Players Cooperate. Math Meth Oper Res 63, 435–442 (2006). https://doi.org/10.1007/s00186-005-0028-2

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  • DOI: https://doi.org/10.1007/s00186-005-0028-2

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