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
Aumann RJ, Drèze JH (1974) Cooperative games with coalition structures. International Journal of Game Theory 3:217–237
Aumann RJ, Maschler M (1985) Game-theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36:195–213
Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logistics Quarterly 12:223–259
Dubey P, Neyman A (1984) Payoffs in nonatomic economies: an axiomatic approach. Econometrica 52:1129–1150
Hart S (1985) An axiomatization of Harsanyi's non-transferable utility solution. Econometrica 53:1295–1313
Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York
Maschler M, Peleg B (1967) The structure of the kernel of a cooperative game. SIAM Journal of Applied Mathematics 15:569–604
Maschler M, Peleg B, Shapley LS (1972) The kernel and the bargaining set for convex games. International Journal of Game Theory 1:73–93
Owen G (1982) Game theory, 2nd ed. Academic Press, New York
Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17:1163–1170
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
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)
Thomson W (1983) Axiomatic bargaining with a variable population: a survey of recent results. Department of Economics, University of Rochester, USA
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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