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On the reduced game property and its converse

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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.

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References

  • Aumann RJ (1985) An axiomatization of the non-transferable utility value. Econometrica 53: 599–612

    Google Scholar 

  • Aumann RJ, Drèze JH (1974) Cooperative games with coalition structures. International Journal of Game Theory 3:217–237

    Google Scholar 

  • Aumann RJ, Maschler M (1985) Game-theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36:195–213

    Google Scholar 

  • Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logistics Quarterly 12:223–259

    Google Scholar 

  • Dubey P, Neyman A (1984) Payoffs in nonatomic economies: an axiomatic approach. Econometrica 52:1129–1150

    Google Scholar 

  • Hart S (1985) An axiomatization of Harsanyi's non-transferable utility solution. Econometrica 53:1295–1313

    Google Scholar 

  • Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York

    Google Scholar 

  • Maschler M, Peleg B (1967) The structure of the kernel of a cooperative game. SIAM Journal of Applied Mathematics 15:569–604

    Google Scholar 

  • Maschler M, Peleg B, Shapley LS (1972) The kernel and the bargaining set for convex games. International Journal of Game Theory 1:73–93

    Google Scholar 

  • Owen G (1982) Game theory, 2nd ed. Academic Press, New York

    Google Scholar 

  • Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17:1163–1170

    Google Scholar 

  • 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 307–317

    Google Scholar 

  • 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 

  • Thomson W (1983) Axiomatic bargaining with a variable population: a survey of recent results. Department of Economics, University of Rochester, USA

    Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel

    B. Peleg

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  1. B. Peleg
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Additional information

This research was partially supported by The Institute for Advanced Studies, The Hebrew University, 91904 Jerusalem, Israel, during 1979–1980.

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Peleg, B. On the reduced game property and its converse. Int J Game Theory 15, 187–200 (1986). https://doi.org/10.1007/BF01769258

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  • DOI: https://doi.org/10.1007/BF01769258

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