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Strong convexity of NTU games

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Abstract

In this article, we provide an alternative notion of NTU convexity: strong ordinal convexity. We show that if a game is strongly ordinal convex, then any marginal vector is in the core, and any marginal payoff is increasing. Some economic examples satisfy this convexity.

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References

  • Greenberg J (1985) Cores of convex games without side payments. Math Oper Res 10: 523–525

    Article  Google Scholar 

  • Hendrickx R, Timmer J, Borm P (2000) On convexity for NTU-games. Tilburg University, CentER working paper no. 2000-108. http://ssrn.com/abstract=250792 or doi:10.2139/ssrn.250792

  • Hendrickx R, Timmer J, Borm P (2002) A note on NTU convexity. Int J Game Theory 31: 29–37

    Article  Google Scholar 

  • Ichiishi T (1981) Super-modularity: applications to convex games and to the greedy algorithm for LP. J Econ Theory 25: 283–286

    Article  Google Scholar 

  • Ichiishi T (1993) The cooperative nature of the firm. Cambridge University Press, Cambridge

    Google Scholar 

  • Lovász L (1983) Submodular functions and convexity. In: Bachem A, Grötschel M, Korte B (eds) Mathematical programming: the state of the art. Springer, New York, pp 235–257

  • Masuzawa T (2003) Punishment strategies make the α-coalitional game ordinal convex and balanced. Int J Game Theory 32: 479–483

    Google Scholar 

  • Milgrom P, Shannon C (1996) Generalized convex games, Berkley University. http://elsa.berkeley.edu/users/cshannon/wp/core.pdf

  • Peleg B (1984) Game theoretic analysis of voting in committees. Cambridge University Press, Cambridge

    Google Scholar 

  • Peleg B (1986) A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution. Math Soc Sci 11: 83–87

    Article  Google Scholar 

  • Shapley L (1971) Cores of convex games. Int J Game Theory 1: 11–26

    Article  Google Scholar 

  • Sharkey W (1981) Convex games without side payments. Int J Game Theory 10: 6–101

    Article  Google Scholar 

  • Vilkov VB (1977) Convex games without side payments. Vestnik Leningradskiva Universitata. vol 7, pp 21–24 (in Russian)

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  1. Faculty of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Takuya Masuzawa

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  1. Takuya Masuzawa
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Correspondence to Takuya Masuzawa.

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Masuzawa, T. Strong convexity of NTU games. Int J Game Theory 41, 699–705 (2012). https://doi.org/10.1007/s00182-012-0330-1

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  • DOI: https://doi.org/10.1007/s00182-012-0330-1

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