Bargaining solutions via surface measures

Arbeitspapier

We introduce a generalization of the Maschler--Perles bargaining solution to smooth bargaining problems for $n$ players. We proceed by the construction of measures on the Pareto surface of a convex body. The MP surface measure is defined for Cephoids, i.e., Minkowski sums of simplices (see [14] for a coherent description); this measure cannot directly be extended to a smooth Pareto surface. Therefore, we introduce a further extension of the Maschler--Perles idea to Pareto surfaces of convex bodies. This extension is suggested by the density $\sqrt[n]{n_1\cdots n_n }$ of normals in coordinate directions -- a term generalizing the Maschler--Perles line integral of $\sqrt{-dx_1 dx_2}$ -- the "donkey cart" in their interpretation. The "deGua'' measure defined this way, is then verified to be the limiting measure of the MP measures along the filter of convergent Cephoids as established in [15].

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Center for Mathematical Economics Working Papers ; No. 658

Klassifikation und Themen

• Klassifikation: Wirtschaft

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Rosenmüller, Joachim
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Center for Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2021

Weitere Informationen

• Handle: http://hdl.handle.net/10419/249881
• URN: urn:nbn:de:0070-pub-29594673
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ