Chapters in Game Theory pp 99-120

Part of the Theory and Decision Library C: book series (TDLC, volume 31) | Cite as

Consistency and Potentials in Cooperative TU-Games: Sobolev’s Reduced Game Revived

  • Theo Driessen


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  1. Calvo, E., and J.C. Santos (1997): “Potentials in cooperative TU-games,” Mathematical Social Sciences, 34, 175–190.CrossRefMathSciNetGoogle Scholar
  2. Dragan, I. (1996): “New mathematical properties of the Banzhaf value,” European Journal of Operational Research, 95, 451–463.CrossRefMATHGoogle Scholar
  3. Driessen, T.S.H. (1988): Cooperative Games, Solutions, and Applications. Dordrecht: Kluwer Academic Publishers.Google Scholar
  4. Driessen, T.S.H., (1991): “A survey of consistency properties in cooperative game theory,” SIAM Review, 33, 43–59.CrossRefMathSciNetMATHGoogle Scholar
  5. Driessen, T.S.H., and E. Calvo (2001): “A multiplicative potential approach to solutions for cooperative TU-games,” Memorandum No. 1570, Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands.Google Scholar
  6. Dubey, P., A. Neyman, and R.J. Weber (1981): “Value theory without efficiency,” Mathematics of Operations Research, 6, 122–128.MathSciNetGoogle Scholar
  7. Hart, S., and A. Mas-Colell (1989): “Potential, value, and consistency,” Econometrica, 57, 589–614.MathSciNetGoogle Scholar
  8. Maschler, M. (1992): “The bargaining set, kernel, and nucleolus,” in: Aumann, R.J., and S. Hart (eds.), Handbook of Game Theory with Economic Applications, Volume 1. Amsterdam: Elsevier Science Publishers, 591–667.Google Scholar
  9. Myerson, R. (1980): “Conference structures and fair allocation rules,” International Journal of Game Theory, 9, 169–182.CrossRefMathSciNetMATHGoogle Scholar
  10. Ortmann, K.M. (1998): “Conservation of energy in value theory,” Mathematical Methods of Operations Research, 47, 423–450.CrossRefMathSciNetMATHGoogle Scholar
  11. Ortmann, K.M. (2000): “The proportional value for positive cooperative games,” Mathematical Methods of Operations Research, 51, 235–248.MathSciNetMATHGoogle Scholar
  12. Sánchez S. F. (1997): “Balanced contributions in the solution of cooperative games,” Games and Economic Behavior, 20, 161–168.MathSciNetGoogle Scholar
  13. Shapley, L.S. (1953): “A value for n-person games,” Annals of Mathematics Studies, 28, 307–317.MathSciNetMATHGoogle Scholar
  14. Sobolev, A.I. (1973): “The functional equations that give the payoffs of the players in an n-person game,” in: Vilkas. E. (ed.), Advances in Game Theory. Vilnius: Izdat. “Mintis”, 151–153.Google Scholar

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© Kluwer Academic Publishers 2002

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  • Theo Driessen

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