A note on external angles of the core of convex TU games, marginal worth vectors and the Weber set

• Danilov VI, Koshevoi GA (2000) Cores of cooperative games, superdifferentials of functions, and the Minkowski difference of sets. J Math Anal Appl 247:1–14

  Article  Google Scholar 

• Demyanov VF, Rubinov AM (1995) Constructive nonsmooth analysis. Verl. Peter Lang, Frankfurt a/M

• Dragan I, Potters J, Tijs S (1989) Superadditivity for solutions of coalitional games. Lib Math 9:101–110

  Google Scholar 

• Gajdos T, Haqyashi T, Tallon JM, Vargnaud JC (2008) Attitude toward imprecise information. J Econ Theory 140:27–65

  Article  Google Scholar 

• González-Díaz J, Sánchez-Rodríguez E (2008) Cores of convex and strictly convex games. Games Econ Behav 62:100–105

  Article  Google Scholar 

• Grünbaum B (2003) Convex polytopes, graduate texts in mathematics, vol 221, 2nd edn. Springer, Berlin

  Book  Google Scholar 

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

  Google Scholar 

• Kuipers J, Vermeulen D, Voorneveld M (2010) A Generalization of the Shapley-Ichiishi result. Int J Game Theory 39:585–602

  Article  Google Scholar 

• Pechersky S (1990) Analysis of cooperative games. In: Demyanov VF, Rubinov AM (eds) Foundations of nonsmooth analysis and quasidifferential calculus. Nauka, Moskow, pp 382–394 (in Russian)

• Pechersky S (2002) The Steiner point of a convex set and the cooperative games solutions. In: Game theory and applications: proceedings of the international congress of mathematicians 2002 satellite conference on game theory and applications. Qingdao University, Qingdao, P.R. China, pp 637–641

• Peleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluver, Dorderecht

  Book  Google Scholar 

• Rockafellar RT (1997) Convex analysis. Princeton University Press, Princeton

  Google Scholar 

• Rosenmüller J (1981) The theory of games and markets. North-Holland, Amsterdam

  Google Scholar 

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

  Article  Google Scholar 

• Shephard GC (1966) The Steiner point of a convex polytope. Can J Math 18:1294–1300

  Article  Google Scholar 

• Vasil’ev VA (1981) About one class of imputations in cooperative games. Dokl Akad Nauk SSSR 256:256–286 (in Russian)

  Google Scholar 

• Weber RJ (1988) Probabilistic values for games. In: Roth AE (ed) The Shapley value (Essays in Honor of Lloyd S. Shapley). Cambridge University Press, Cambridge, pp 101–119

  Chapter  Google Scholar 

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