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Title: Path monotonicity, consistency and axiomatizations of some weighted solutions
Author: Calleja, Pere
Llerena Garrés, Francesc
Keywords: Jocs cooperatius (Matemàtica)
Lògica matemàtica
Economia matemàtica
Cooperative games (Mathematics)
Mathematical logic
Mathematical economics
Issue Date: Mar-2019
Publisher: Springer Verlag
Abstract: On the domain of cooperative games with transferable utility, we introduce path monotonicity, a property closely related to fairness (van den Brink, in Int J Game Theory 30:309-319, 2001). The principle of fairness states that if a game changes by adding another game in which two players are symmetric, then their payoffs change by the same amount. Under efficiency, path monotonicity is a relaxation of fairness that guarantees that when the worth of the grand coalition varies, the players' payoffs change according to some monotone path. In this paper, together with the standard properties of projection consistency (Funaki, in Dual axiomatizations of solutions of cooperative games. Mimeo, New York, 1998) and covariance, we show that path monotonicity characterizes the weighted surplus division solutions. Interestingly, replacing projection consistency by either self consistency (Hart and Mas-Colell, in Econometrica 57:589-614, 1989) or max consistency (Davis and Maschler, in Nav Res Logist Q 12:223-259, 1965) we obtain new axiomatic characterizations of the weighted Shapley values and the prenucleolus, respectively. Finally, by the duality approach we provide a new axiomatization of the weighted egalitarian non-separable contribution solutions using complement consistency (Moulin, in J Econ Theory 36:120-148, 1985)
Note: Versió postprint del document publicat a:
It is part of: International Journal of Game Theory, 2019, vol. 48, num. 1, p. 287-310
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ISSN: 0020-7276
Appears in Collections:Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

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