International Journal of Game Theory

, Volume 15, Issue 3, pp 187–200

On the reduced game property and its converse

  • B. Peleg
Article

Abstract

We investigate the relationship between two solutions, the core and the prekernel, and reduced games of coalitional games. An axiomatic characterization of these two solutions is obtained by means of the reduced game property and its converse.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann RJ (1985) An axiomatization of the non-transferable utility value. Econometrica 53: 599–612Google Scholar
  2. Aumann RJ, Drèze JH (1974) Cooperative games with coalition structures. International Journal of Game Theory 3:217–237Google Scholar
  3. Aumann RJ, Maschler M (1985) Game-theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36:195–213Google Scholar
  4. Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logistics Quarterly 12:223–259Google Scholar
  5. Dubey P, Neyman A (1984) Payoffs in nonatomic economies: an axiomatic approach. Econometrica 52:1129–1150Google Scholar
  6. Hart S (1985) An axiomatization of Harsanyi's non-transferable utility solution. Econometrica 53:1295–1313Google Scholar
  7. Luce RD, Raiffa H (1957) Games and decisions. Wiley, New YorkGoogle Scholar
  8. Maschler M, Peleg B (1967) The structure of the kernel of a cooperative game. SIAM Journal of Applied Mathematics 15:569–604Google Scholar
  9. Maschler M, Peleg B, Shapley LS (1972) The kernel and the bargaining set for convex games. International Journal of Game Theory 1:73–93Google Scholar
  10. Owen G (1982) Game theory, 2nd ed. Academic Press, New YorkGoogle Scholar
  11. Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17:1163–1170Google Scholar
  12. Shapley LS (1953) A value forn-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317Google Scholar
  13. Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations. Mathematical Methods in the Social Sciences 6:150–165 (in Russian)Google Scholar
  14. Thomson W (1983) Axiomatic bargaining with a variable population: a survey of recent results. Department of Economics, University of Rochester, USAGoogle Scholar

Copyright information

© Physica-Verlag 1986

Authors and Affiliations

  • B. Peleg
    • 1
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael

Personalised recommendations