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2019-03

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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/134622

Path monotonicity, consistency and axiomatizations of some weighted solutions

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https://doi.org/10.1007/s00182-019-006

Resum

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)

Matèries

Jocs cooperatius (Matemàtica), Axiomes, Lògica matemàtica, Economia matemàtica

Matèries (anglès)

Cooperative games (Mathematics), Axioms, Mathematical logic, Mathematical economics

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Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

Citació

CALLEJA, Pere, LLERENA GARRÉS, Francesc. Path monotonicity, consistency and axiomatizations of some weighted solutions. _International Journal of Game Theory_. 2019. Vol. 48, núm. 1, pàgs. 287-310. [consulta: 25 de febrer de 2026]. ISSN: 0020-7276. [Disponible a: https://hdl.handle.net/2445/134622]

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