Abstract
Owen value is an extension of Shapley value for cooperative games when a particular coalition structure or partition of the set of players is considered in addition. In this paper, we will obtain the Shapley value as an average of Owen values over each set of the same kind of coalition structures, i.e., coalition structures with equal number of sets sharing the same size.
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References
Aumann RJ, Drèze JH (1974) Cooperative games with coalition structures. Int J Game Theory 3: 217–237
Dubey P, Neyman A, Weber RJ (1981) Value theory without efficiency. Math Oper Res 6: 122–128
Hart S, Kurz M (1974) Endogenous formation of coalitions. Econometrica 51: 1047–1064
Hart S, Kurz M (1984) Stable coalition structures: coalition and collective action. Physica, Würzburg, pp 235–258
Owen G (1977) Values of Games whit a priori Unions. In: Henn R, Moeschlin O (eds) Essays in mathematical economics and game theory. Fields Institute, Berlin, pp 76–88
Owen G (1981) Modification of the Banzhaf–Coleman index for games with a priori unions. In: Holler MJ (eds) Power, voting and voting power. Physica, Wurzburg
Owen G (1995) Game Theory. 3rd edn. Academic Press, San Diego
Shapley LS (1953) A value for n-Person Games. Study 28. Princeton University Press, Annals of Mathematics Studies, pp 307–317
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López, S., Saboya, M. On the relationship between Shapley and Owen values. Cent Eur J Oper Res 17, 415–423 (2009). https://doi.org/10.1007/s10100-009-0100-8
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DOI: https://doi.org/10.1007/s10100-009-0100-8