Path monotonicity, consistency and axiomatizations of some weighted solutions
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 symmetr...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/134622 |
| Acceso en línea: | https://hdl.handle.net/2445/134622 |
| Access Level: | acceso abierto |
| Palabra clave: | Jocs cooperatius (Matemàtica) Axiomes Lògica matemàtica Economia matemàtica Cooperative games (Mathematics) Axioms Mathematical logic Mathematical economics |
| Sumario: | 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) |
|---|