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Existence of Weakly Cooperative Equilibria for Infinite-Leader-Infinite-Follower Games

  • Zhe YangEmail author
  • Qing-Bin Gong
Article
  • 8 Downloads

Abstract

In this paper, we first generalize Yang and Ju’s (J Glob Optim 65:563–573, 2016) result in Hausdorff topological vector spaces. Second, we introduce the model of leader-follower games with infinitely many leaders and followers, that is, infinite-leader-infinite-follower game. We next introduce the notion of weakly cooperative equilibria for infinite-leader-infinite-follower games and prove the existence result.

Keywords

(Weakly) cooperative equilibrium Infinite-leader–infinite-follower game Existence 

Mathematics Subject Classification

91A10 91A12 91A40 

References

  1. 1.
    Pang, J.S., Fukushima, M.: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader–follower games. Comput. Manag. Sci. 2(1), 21–56 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Yu, J., Wang, H.L.: An existence theorem of equilibrium points for multi-leader–follower games. Nonlinear Anal. Theory Methods Appl. 69(5–6), 1775–1777 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hu, M., Fukushima, M.: Variational inequality formulation of a class of multi-leader–follower games. J. Optim. Theory Appl. 151(3), 455–473 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ding, X.P.: Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces. J. Glob. Optim. 53(3), 381–390 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jia, W.S., Xiang, S.W., He, J.H., Yang, Y.L.: Existence and stability of weakly Pareto–Nash equilibrium for generalized multiobjective multi-leader–follower games. J. Glob. Optim. 61(2), 397–405 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Aumann, R.J.: The core of a cooperative game without side payments. Trans. Am. Math. Soc. 98, 539–552 (1961)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Scarf, H.E.: On the existence of a cooperative solution for a general class of \(n\)-person games. J. Econ. Theory 3, 169–181 (1971)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kajii, A.: A generalization of Scarf’s theorem: an \(\alpha \)-core existence theorem without transitivity or completeness. J. Econ. Theory 56, 194–205 (1992)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Askoura, Y., Sbihi, M., Tikobaini, H.: The ex ante \(\alpha \)-core for normal form games with uncertainty. J. Math. Econ. 49, 157–162 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Noguchi, M.: Cooperative equilibria of finite games with incomplete information. J. Math. Econ. 55, 4–10 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Noguchi, M.: Alpha cores of games with nonatomic asymmetric information. J. Math. Econ. 75, 1–12 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Askoura, Y.: An interim core form normal form games and exchange economies with incomplete information. J. Math. Econ. 58, 38–45 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Askoura, Y.: The weak-core of a game in normal form with a continuum of players. J. Math. Econ. 47, 43–47 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Askoura, Y.: On the core of normal form games with a continuum of players. Math. Soc. Sci. 89, 32–42 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yang, Z.: Some infinite-player generalizations of Scarf’s theorem: finite-coalition \(\alpha \)-cores and weak \(\alpha \)-cores. J. Math. Econ. 73, 81–85 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yang, Z.: Some generalizations of Kajii’s theorem to games with infinitely many players. J. Math. Econ. 76, 131–135 (2018)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Yang, Z., Ju, Y.: Existence and generic stability of cooperative equilibria for multi-leader–multi-follower games. J. Glob. Optim. 65, 563–573 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Martins-da-Rocha, V.F., Yannelis, N.: Nonemptiness of the alpha-core. Fgv/epge Economics Working Papers (2011).  https://doi.org/10.1107/S0567740869005723
  19. 19.
    Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhikers Guide. Springer, Heidelberg (2006)zbMATHGoogle Scholar

Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of EconomicsShanghai University of Finance and EconomicsShanghaiChina
  2. 2.SUFE Key Laboratory of Mathematical Economics, Ministry of EducationShanghaiChina

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